Product Description
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 —Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory—Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Phillip Griffiths & Joseph Harris Principles of Algebraic Geometry Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I—Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II—Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1—Power Series—Integration—Conformal Mapping—Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2—Special Functions—Integral Transforms—Asymptotics—Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3—Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin O. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Ali Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P. M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I—Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II—Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III—Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems ... Read more

Customer Reviews (7)

Best introduction to integration theory.
This is a great introduction to integration theory, and probably the only book that is suitable for (1) a one semester course, and (2) a wide audience.The topics presented in this book are the main concepts ("work horse material") of integration and measure.I highly recommend this book as an introduction or tag along book for mathematicians (analysts), and as a primary book to learn the material for students in economics, electrical engineering, and statistics.

A good introduction: concise and clear.
The book is concise and easy to follow.The author rarely gives lengthy explanations and analogies, but spends the bulk of the book stating solid facts and proofs.I also like the organization of the book.All definitions and theorems are explicitly stated and indexed, not scattered in paragraphs in the body of the text.

The book misses subjects such as complex measures (they are briefly mentioned), the fundamental theorem of calculus under Lebesgue settings, and probability measures, but its ok since the book is an introduction to the subject.A more comprehensive (and harder to read) book is "Real & Complex Analysis" by Walter Rudin.If you are interested in probability, consider Ptrick Billingsley's book "Probability and Measure".

Good Integration and Measure Into (A Bit Expensive Though)
The exposition of integration in this book is the clearest I have read. I also found the chapter on modes of convergence, where it laid out the relationship between things such as L^P-convergence and convergence in measure, to be extremely useful. The second half, where it covers topics like Lebesgue measure, repeats some of the same information from the first part which is a bit iritating if you are reading straight throught, but contains a lot of good information. The book is also quite small making it easy to take with you as a quick reference.

Let me warn you though that this is an introduction to integration and measure _not_ an introduction to real analysis. It does not cover important topics like L^P-approximation, differentiation, etc. For a complete treatment of real analysis, I recommend the books "Lebesgue Integration on Euclidean Space" by Frank Jones and the slightly more abstract "Real and Functional Analysis" by Serge Lange.

IF YOU WANT TO UNDERSTAND MEASURE THEORY...
IF YOU WANT TO UNDERSTAND MEASURE THEORY READ THIS BOOK, MAYBE THE ONLY PROBLEM IS THE LACK OF EXAMPLES BUT THE WAY THAT THE THEORY IS PRESENTED MAKE IT YOUR FIRST CHOICE WHEN YOU TRY TO LEARN MEASURE THEORY.

Excellent as an itroduction and as a reference
When I took my first one-semester course on measure and Lebesgue integration my teacher chose Bartle's "The Elements of Integration" as text. After reading many other books on the subjectnow I'm sure he made a wise decision.

Assuming almost no strongmathematical background, Bartle is able to build up the basic Lebesgueintegral theory introducing the fundamental abstract concepts(sigma-algebra, measurable function, measure space, "almosteverywhere", step function, etc.) in such an easy way that the studentis not only able to handle them but to UNDERSTAND them.

From the firstpart of the book I appreciate specially chapters 6, 7, and 10, on L_pspaces, modes of convergence, and product measures, respectively. Thesechapters contain the most used results of the basic theory, and they arestated exactly in the way one needs them, making the book very useful forfuture reference.

I like the second part very much also, because itstresses the importance of measure theory by itself and not only as arequisite for integration theory. If you are interested in fractal geometryor geometric measure theory you will find chapters 11 to 17 veryhelpful.

Since I own this book it has never been lazy in my bookshelf. ... Read more

Product Description

Customer Reviews (3)

Fatal inaccuracies
There's a stupid mistake in the first set of examples on page 16: 1 (vi) should be subset not equality. He also uses seriously non-standard notation for sets and spaces and so on. Don't let it slow you down.

Something new in measure theory here
The book isn't organized as a teaching text: is is a definition, theorem and proof type structure that is pretty hard reading. I would have given it two stars except for the convergence diagrams which are digraphs showing the connections between types of convergence. I don't know if the author invented it , but it seems to be a new way to visualize sequence convergence
processes that I hadn't seen before.
He gets low marks for leaving out Hardy, Hilbert and Banach in his discussion of measure spaces. The place of measure in topology
is also not well discussed. Lebesque measure ideas and integration theories
are well discussed.

Something new in measure theory here
The book isn't organized as a teaching text: is is a definition, theorem and proof type structure that is pretty hard reading. I would have given it two stars except for the convergence diagrams which are digraphs showing the connections between types of convergence. I don't know if the author invented it , but it seems to be a new way to visualize sequence convergence
processes that I hadn't seen before.
He gets low marks for leaving out Hardy, Hilbert and Banach in his discussion of measure spaces. The place of measure in topology
is also not well discussed. Lebesque measure ideas and integration theories
are well discussed. ... Read more

Product Description
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians. ... Read more

Customer Reviews (3)

Good book for non-analysts
Great book for graduate students in statistics and electrical engineering.Author provides a good set of topics written in an accessible manner, including explicit proofs.In an ideal world on would get to spend a year studying this book before taking a measure theoretic probability course.It would be difficult to beat this book in general, and for the price it is even tougher.An alternative, which is a shorter book but contains some different topics of particular interest in probability, is "Measure Theory" by Donald L. Cohn.I don't know if I could recommend one over the other, but if you were to buy two books, these are probably the two you want.

10/10
Olcu teorisi ve integrasyon uzerine yazilmis kitaplar arasinda kesinlikle acik ara onde Yeh 'in kitabi, Rudin,Bartle ya da Royden 'in kitaplarindaki önemli teoremlerin veispatlarin okuyucuya birakma veya ispatlari atlayarakhizlica gecme gelenegi kesinlikle yok. Butun ispatlar derinlemesine ve ciddi anlamda tatmin edici. Ancak genede soyut yapi ilk okuyanlarin gözünü korkutabilir, ancak kesinlikle vazgecilmemesi gereken bir kitap. 4. bölümdeki Klasik Banach Uzaylari bölümünün ilk birkaç altbölümü ise fonksiyonel analize giris saglamasi yönünden önemli.

Hernekadar gereginden çok daha fazlasini da içerse ve çalisirken belli bir noktadan sonra detaylardan dolayi yorsa da bastan sona okunmasi daha ileriki konularin daha net sekilde anlasilmasi icin gerekiyor

A gemstone for students
This book covers a lot of material on measure and integration and the author wrote certainly one of the most solicitous book in this subject.

Over 700 pages long, this book will surely cover all the contents of a classical course on measure and integration theory. All explanations and proofs are written in a highly didactical way. This means that the author did not care much about conciseness, and took a great amount of work by choosing good notations and developing his arguments caring with the student understanding in mind. Other books on the subjects are mostly too concise in their explanations or do not cover too many topics or ,wrose, are not written with the sufficient care to be called a didactic book.

The result is a elegant, encyclopedic and useful book on understanding the basics of measure and integration.


... Read more

Product Description
Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material. ... Read more

Customer Reviews (15)

Do not use it alone
The books provides a good introduction. However this should not be your primary book for the subject matter. It is an awesome book to get your feet wet a little. After the first 3 chapters, I suggest looking at books that are more specialized. If you have access to a University library, then there are many books on this that does much better job on introduction. For others, this could be the next best alternative.

They need to inform customers of what they get through Amazon upgrade...(Please read before saying "Irrelevant")
To other customers of Amazon bookstore- First of all, I apologize for writing more about the service of Amazon than about the book itself. If I knew any other place to complain about their service, I would've done so. Still, I suspect that what I write below may be useful to anyone who is considering to pay for the so-called Amazon upgrade.

I think the book itself to be very nice (although I could not study the later half of the book). For a starter, the authors point out several problems of Riemann integration; so, the reader can understand why we need a more complex, but also more general, method for integration. Next, they explain important concepts: outer measure function m*, measurable sets, Borel sets, and so on. Then, they introduce the reader to Lebesgue integration. Their construction of Lebesgue integral is similar to that of Kolmogorov, but it is more elegant and conceptually lucid. As a self-studying beginner, I found their approach to be pedagogically efficient, because I could see where they were (or I was) going.

Unfortunately, I had to stop in the middle of Chapter 4. It was because I paid for the so-called Amazon upgrade, and sold my paper copy, but all of sudden, they blocked my access to the digital copy. I emailed twice to ask why, but each time they sent a very short reply, which only explains where I can find the digital copy of my book. Since I already knew that information, I had to dig into the deep part of FAQ about Amazon upgrade. As it turned out, they blocked my access because I read the book on more than seven different computers within one month. It is a restriction imposed by the publisher.

Fair enough, but my complaint is "Why didn't they inform me of this restriction when I was paying?" Also, I emailed them to unlock my library, which contains two other books, but they have sent the same email about "Where you can find the digital copy..." So I am stuck in this situation.

Again, I am sorry for writing about a problem of Amazon upgrade rather than the book itself. However, this problem can be yours too, if you pay for Amazon upgrade. So before you pay, be aware that your access to your own book may be arbitrarily limited by the publisher or Amazon.

Great For Self Study
I highly recommend this book as a supplement or for self study. However, I do not recommend it be used as textbook in a course. Solutions are in the back on the text. I really love this book though.

absolutely useless
It starts out okay, good overview of measurable sets and the like.However, it does not even have the essential core theorem to the discipline stating when it is possible to integrate a function!one of the great thing about Lebesgue integration is that a function is integrebale in this sense IF AND ONLY IF the function is measurable. thats the whole point of having measurable functions.there is no if and only if theorem for RS integration.Plus other things, like it talks vaguely about 'randomly choosing a point' but with no precise definition.Things like that.

You are better off buying a classic by Halsey Royden or Walter Rudin, or something like that.This book is useless.

Excellent Book
The text is written at a level which is suitable for the classroom or self-teaching by an advanced student.The authors spare few details.I am very satisfied with my purchase. ... Read more

Product Description

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.

After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.

As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.

Also available, the first two volumes in the Princeton Lectures in Analysis: ... Read more

Customer Reviews (6)

Great book
This book is very nice, concise and still clear to read. I still did not do a lot into it (only chapter one so far).
I taken a course in Analysis before and decided to read this book just to review and to study the subject through a different perspective.

Not as good as the classics
I just completed a first-semester graduate course in which we used this textbook, and I was very disappointed by this choice. The authors too often gloss over details and omit definitions. Plus there are a few minor mistakes or non-standard definitions (check out the definition of "limit point" on page 3!). It reads much more like a lecture than a textbook, and I found it frustrating not to have a thorough resource to fall back on when my own professor's lecture was unclear. I have always prided myself in my ability to learn from a textbook, as I had no difficulty following Munkres in his "Topology" or Dummit and Foote in their "Abstract Algebra." However, I found this real analysis text to be quite challenging to follow time and time again--even our professor commented on how some proofs were unnecessarily complicated and how certain "trivial" details that had been omitted were not quite so trivial and indeed deserved mention. The only reason I did not give this book one star is that I found the problems to be good.

I am getting ready to purchase a copy of Royden's "Real Analysis" to help me study for my qualifying exam. I wish we had used it all along!

great book
i found the first three chapters of this book very clear and well written. i'd strongly recommend it for someone looking to learn about analysis on the real line.

Good book for reading and as a graduate student
Easy to read. My university is using this book to get the graduate students ready for the real analysis qualifying exam. So go ahead and buy this book if you're planning to work on a PhD in mathematics. If you're not planning to work on a PhD in math, this is still a good book to read if you enjoy studying about the real line.

The book begins with measure theory, integration and differentiation. These are included in Chapters 1 to 3. Then in Chapters 4 and 5, we look into Hilbert spaces. This is similar to studying finite-dimensional inner-product spaces, but here, Hilbert space is infinite-dimensional. However, the analysis is very similar. If you know some linear algebra, it should feel like as if you have already read these two chapters.

Finally in Chapters 6 and 7, we see abstract measure theory, including Hausdorff measure, and we study fractals and self-similar sets. And this concludes the book.

Also recommend Walter Rudin's Real Analysis.

Suffers from all the flaws of a 1st edition
This book has a lot of problems. Several sections are poorly written/edited. Several important named theorems are not clearly labeled. Also some of the proofs contain typos or errors. The chapter on differentiation is particularly lacking. The chapter is poorly organized and presented. There is also a glaring TeX error in the chapter.

At Princeton this book is used as part of an undergraduate course, and it shows. This is not the ideal book for a graduate level course in real analysis(though I think it would be very well suited for advanced undergrads). Too much time is spent on Lebesgue measure and integration in the first 2 chapters, and abstract measure theory is not intoduced until chapter 6. Also the Monotone Class theorem is lacking from the chapter on abstract measure theory. Also, the book only touches on functional analysis in the two chapters on Hilbert spaces (where they assume all Hilbert spaces are separable).

On the other hand, the presentations of Lebesgue measure/integration and Hilbert spaces in the book are pretty good. The exercises and problems in teh book (when stated properly) are very good and instructive. Overall this book has a lot of potential to be very good, but seems to be suffering from a lack of revision. Hopefully these issues will be fixed in later editions. ... Read more

Product Description
Intended as a straightforward introduction to measure theory, this textbook emphasizes those topics relevant and necessary to the study of analysis and probability theory. The first five chapters deal with abstract measure and integration. At the end of these chapters, the reader will appreciate the elements of integration. Chapter 6, on differentiation, includes a treatment of changes of variables in Rd. A unique feature of the book is the introductory, yet comprehensive treatment of integration on locally Hausdorff spaces, of the analytic and Borel subsets of Polish spaces, and of Haar measures on locally compact groups. Measure Theory provides the reader with tools needed for study in several areas of current interest, in particular harmonic analysis and probability theory, and is a valuable reference tool. ... Read more

Customer Reviews (7)

A good introduction to Measure Theory
I used this book for my graduate measure theory class. We covered the first seven chapters. The book is written in a clear fashion and is easy to follow. It is concise and at the same time is almost self contained.

The first chapter gives an introduction to measure theory. It deals with sigma algebras, measures, outer measures, completeness and regularity. The lebesgue measure is also introduced in this chapter.

The second chapter starts of measurable functions. It then proceeds to almost sure properties followed by integration. These are followed by the theorem: Monotone convergence theorem, Beppo Levi theorem, Fatou's Lemma and Dominated Convergence Theorem. The chapter also discusses briefly on Riemann integrals.

The third chapter is on different modes of convergence. It proves the Egoroff theorem. This is followed by the definition and properties of Banach spaces.

The fourth chapter discusses signed measures. The Hahn decomposition theorem and Jordan decomposition theorems are proved. It is followed by absolutely continuous measures which leads to Radon-Nikodym theorem.

The fifth chapter deals with Product measures. The most important theorem in this chapter is the Fubini's theorem which is proved in the second section.

The sixth chapter is on differentiation of measures. Proves Fundamental theorem of calculus.

The seventh chapter is on Hausdorff spaces and Riesz representation theorem followed by properties of regular measures (Lusin's theorem)

Chapter 8 is on Polish Spaces and Analytic Sets

Chapter 9 is on Haar Measures

(We did not cover the last two chapters in this course)

A great companion to Folland or Rudin
I believe that Cohn's Measure Theory is a fantastic companion for learning Analysis in concert with one of the denser books from Folland or Rudin. While still covering a wide range of subjects, Cohn's exposition is much more conducive to the learning experience than either of the other two, in my opinion. He does an excellent job of explaining his reasoning in proofs, while still leaving enough to the reader to get them involved in the process.

The exercises are also very well done, and range over a wide difficulty level, though are easier, on the whole, than those in the other two books.

This book, even by itself, will give you a VERY strong foundation in measure theory and integration theory, and has the benefit of being very affordable.

A Book of Clarity and Rigor
Cohn's Measure Theory is one of the most clear, rigorous and easy-going textbooks I have ever read. All theorems, propositions, lemmas are stated in full; there is neither a missing hypothesis, nor an obscure conclusion. Moreover, the number of errors in the book is minimal when compared to other texts in mathematics.

I like
Very technical yet readable book. Cohn does a great job in the explanation of integrability. The appendix is very complete and gives you a first hand help on the topics discussed trough out the book. I used the book for Real Analysis and it has been of great help.

The book is very good, but Amazon's digital upgrade is very poor
I bought the book, and also the Amazon upgrade to digital version, so I could read the book online. It was a great disappointment. The viewing screen is so small that it cannot show a full page; I tried to print out a few pages, but the printing software froze my printer; and then the program cut me off, claiming I had exceeded the limits, which I had not been told about. I tried to get a refund a few hours after I had bought it, but customer service was unhelpful. They didn't even know what an Amazon Book Upgrade was, and then they claimed, mistakenly, that upgrades cannot be returned. Finally, they told me I had viewed more than the allowance, which was not true. Overall, an awful experience. It's just $10 wasted, but my advice is: DON'T GET THE UPGRADE. ... Read more

Product Description
Measure theory and integration are presented to undergraduates from the perspective of probability theory. In fact, discrete probability theory is taught at many institutions as a freshman course. The early chapters, going under the rubric of the law of large numbers, show why measure theory is needed for the formulation of problems in probability, and explain why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measure-theoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on Rn (metric space approach), the Borel-Cantelli lemmas, straight measure theory (the Lebesgue integral). In this concise text, a number of applications to probability are packed into the exercises. ... Read more

Customer Reviews (2)

Graduate Measure Theory w.r.t. Probability
When I first looked through this book, I thought it was horrible. After looking through it more and more, I got to like it more. It's not a bad book after all. The book says that it's for undergraduates, but I think it's for graduate students. This is the book used most often at URI for graduate measure theory and integration. I think many of the problems in the book are very challenging considering that the explanations in the book are not very detailed. I would rate this book 3 and 1/2 stars if possible, but I gave it four. It's not the best, but it's an alright book.

Great Introduction to Measure Theory
This book is great. As an undergraduate I did an independent study using this book and learned lots of stuff. The exposition is nicely done and allows for a clear presentation of some very complicated ideas. There are also lots of great examples and applications, which can be really helpful when dealing with something as abstract as measure theory. The exercises mix well with the exposition and contain interesting results. You can learn a great deal from this book without needing to go to lectures, but it does help a lot to be able to ask somebody questions as the material gets quite tricky sometimes.

One thing that could have been done better was Polya's Theorem on random walks. The book didn't get into what happens in dimensions above 2.

It has a great intoduction to Fourier transforms which shows some interesting connections between Fourier series and Probability.

This is a great book if you have some time between undergraduate real analysis and graduate real analysis. Also, you can learn this book right after an undergraduate real analysis course so that you can impress your friends by being the first kid on the block to know about cool stuff like "The Discrete Dirchlet Problem" or how to prove the Weierstrauss Approximation Theorem by using the Law of Large Numbers. It's also cheap. ... Read more

Product Description
This book gives a straightforward introduction to the field, as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author’s earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem.

The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin’s theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory.

The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course. ... Read more

Product Description
A superb text on the fundamentals of Lebesgue measure and integration.

This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.

Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed. ... Read more

Product Description
Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given. ... Read more

Customer Reviews (3)

Good Attempt, Flawed Presentation
At first glance the book seems to be great.It's something less than a textbook, making it more approachable to the "beginner" (as the book calls it).One must wonder, however, what exactly the beginner wants.

One thing the beginner apparently does NOT want is mathematical rigor, which the book applies inconsistently.Some basic theorems are given pages upon pages of proof, while more difficult theorems are not only not proven (the author recommends a "classical textbook" for the "experienced reader") but not even stated specifically.Furthermore several of the proofs that are supplied (which are probably assumed to be "classical" and therefore not edited) are actually flawed, relying on circular logic or jumps which are not actually logically valid.

The last qualm I have with the book is that they are so lax with notationthat many theorems appear to mean something completely other than what they appear to (especially concerning higher-dimensional spaces).This may be a product of this book being essentially unchanged in thirty years.

After all these complaints I will say that when the book gets it right, as it often does, it is easy to read and understandable.So long as it is not examined too closely.

Great book
Its a very good text for a first meeting on Lebesgue integration, measure and functional analysis. Rigorous, elegant and simple. A quality book for pure and applied mathematics.

However I found two little mistakes:

In page 151, in the proof of the integral of a transformation, he makes use of the Dominated Convergence Theorem two times (one first time, at the begining of page 151, is right). Thats wrong because we can't "dominate" the function "g" when K -> inf. The correct proof involves divide the function in positive and negative parts and then aplicate Monotone Convergence Theorem. The same in the end of the proof when he generalizes to infinite measure sets.

In page 157, equation (7) should be verified when ||h||<2*delta, not ||h||Anyway, a brilliant text. Purchase it.

Good introduction to the theory of Lebesgue integration
I picked up this book on a trip to London. I've known some complex analysis and real analysis, and I decided to learn some Lebesgue on my own; ergo the purchase of this book. The style of writing is very lucid: quite informal at times, and the math part is really well-presented (the explanation on 'measure zero' set, for example, is clear, and mathematically rigorous). The topics chosen are not in-depth (I learnt much more on the topic during an actual course in college), but the book definitely works well as a supplement reading, when you are taking real analysis course. ... Read more

Product Description
A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis

Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis.

The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes:

• Measure spaces, outer measures, and extension theorems

• Lebesgue measure on the line and in Euclidean space

• Measurable functions, Egoroff's theorem, and Lusin's theorem

• Convergence theorems for integrals

• Product measures and Fubini's theorem

• Differentiation theorems for functions of real variables

• Decomposition theorems for signed measures

• Absolute continuity and the Radon-Nikodym theorem

• Lp spaces, continuous-function spaces, and duality theorems

• Translation-invariant subspaces of L2 and applications

The book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign.

Providing an efficient and readable treatment of this classical subject, Measure and Integration: A Concise Introduction to Real Analysis is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences. ... Read more

Product Description
Integration is one of the two cornerstones of analysis. Since the fundamental work of Lebesgue, integration has been interpreted in terms of measure theory. This introductory text starts with the historical development of the notion of the integral and a review of the Riemann integral. From here, the reader is naturally led to the consideration of the Lebesgue integral, where abstract integration is developed via measure theory. The important basic topics are all covered: the Fundamental Theorem of Calculus, Fubini's Theorem, $L_p$ spaces, the Radon-Nikodym Theorem, change of variables formulas, and so on.

The book is written in an informal style to make the subject matter easily accessible. Concepts are developed with the help of motivating examples, probing questions, and many exercises. It would be suitable as a textbook for an introductory course on the topic or for self-study.

For this edition, more exercises and four appendices have been added. ... Read more

Customer Reviews (1)

Full of small errors.Excellent, and brilliant book.Very thorough.
This is an amazing book; its clarity is outstanding throughout.However, I want to voice serious reservations about it due to an abundance of errors; I am reviewing the second edition published by the AMS.

This book has more errors than any other math book I have read.These errors include minor typographical errors like sloppy spacing, to equations with the terms included in the wrong order or on wrong lines, misnumbered references to earlier results, and occasional abuse of notation that hinders mathematical rigour.There are substantive errors as well, including the citing of a source for a proof of a theorem that is not actually proved in the cited source.

Errors aside, this is one of the clearest and best motivated expositions of measure theory I have been able to find.The book moves slowly, but never too slowly; it explores essential questions that a student should consider, like counterexamples, converses, and the subtle distinctions between different strengths of conditions.I find this thoroughness very welcome; most texts in measure theory present the most logically direct path to a bare-bones collection of useful results, an approach that doesn't necessarily help students.

The first chapter, on Riemann integration, is unique.The topic is explored in much more depth than in most analysis texts.Most students feel they understand Riemann integration; this book will likely convince them that they do not--and then it will fill the gaps in their understanding.The counterexamples in this book are outstanding--simple, worked through with clarity, and deep.

I think this book would make an outstanding textbook on measure theory, and it is one of the few texts that is good for self-study.I just wish the errors could be corrected; I would then rate it 5 stars without a doubt. ... Read more

Product Description

This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics.

Customer Reviews (1)

Good Book But ...
This is a good book. And the authors try to summary the measure theory and probability theory into one book. Benefit of doing this is easy to see relationship between the two theories more clearly than reading one for each topic. However, I should say that no book trying to do this job is successful, including this one. To my experience, better understand of real analysis is necessary. If you do not, I think this book is not suitable for you. If you do, you can start the book from chapter 6 and treat the 1-5 chapter as a good reference.

Moreover,the statements in this book are quite concise and I like this style. However, this is a quite new one. There are pretty much typos in the book. I expect that the second edition will be much better than this one. ... Read more

Product Description
This paperback, which comprises the first part of Introduction to Measure and Probability by J. F. C. Kingman and S. J. Taylor, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level. It sets the material out in a form which not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material to probability theory and also the basic theory of L2-spaces, important in modern physics. A large number of examples is included; these form an essential part of the development. ... Read more

Product Description
An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics
In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry.
Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include:
* Measurable Functions
* The Lp Spaces
* The Radon-Nikodym Theorem
* Products of Two Measure Spaces
* Arbitrary Products of Measure Spaces
Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics.
In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics. ... Read more

Customer Reviews (1)

The New Standard for Measure Theory Books
This is a fantastic book on measure theory.The focus is on measure theory on its own right and not on probability.I was lucky to come across this book while canvassing the measure theory books at our library.I looked at the books by Billingsley, Halmos, Chung, Resnick, Rao, Rudin, Pollard, Dudley, Nielson, Stroock, Williams, Pitt, and many others.Hand-down, Vestrup is the best.

I believe after scrutinizing so many books, I have a very good baseline to judge Vestrup's work.Here are a few specific reasons:

(1) If you don't like detail and revel in banging your head against the walls to figure out the skipped details in Billingsley, this is not the book for you.But If you are a first timer to measure theory, this is as good as it will get; All the major results of measure theory are presented in detailed and clear manner with few skipped details and few not-so-obvious "it is obvious" remarks.

(2) Vestrup has a lot of exercises with lots of helpful hints.Some problems at first appear to be long and intimidating till you look closely and discover that Vestrup leads you through the problems with his hints.

(3) Certain topics central to understanding of measure theory were given cursory coverage by most of the books mentioned above.Not Vestrup.For example, Vestrup devotes a whole chapter to extensions.This is just one example of many central ideas Vestrup develops meticulously and painstakingly.

This book is fairly new and I think its popularity will grow as more students and professionals discover it.I suppose the only criticism I have is that the typesetting can be improved (second edition maybe?)

There are a few other good books (Ash, Bartle, and Royden) that are out there that you may consider but again Vestrup trumps them all.Whatever you decide on, I strongly warn against using Billingsley. ... Read more

Product Description
This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP. 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure. This approach via integration of elementary functions is particularly well adapted to the proof of Riesz's famous theorems about linear functionals on the classical spaces C (X) and LP and also to the study of topological notions such as Borel measure. This book will be used for final year honours courses in pure mathematics and for graduate courses in functional analysis and measure theory. ... Read more

Product Description
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications.

With more than 170 references for further investigation of the subject, this Second Edition

Customer Reviews (1)

Jon's Review
Simply put, M.M. Rao's "Measure Theory and Integration" is an awesome book.It is truly the "Encyclopedia Britannica" of Real Analysis textbooks. This math textbook/reference book contains the most general, yet practical, theorems on the subject known to mankind.I cannot recommend it highly enough. ... Read more

Product Description

This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in the area and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, and functional analysis. The material is of interest to experts, young researchers and postgraduate students.