Book 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 (6)

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.

A great place to begin
Measure and Integration is a daunting subject for mathematical neophytes.Bartle's little volume is the right place to start.I first learnedmeasure theory from it 20 years ago and went on to study functional analysis and stochastic approximation.

I was able to master thematerial on my own with this book.The problems are at the right level andhe begins with the correct level of abstraction.I recommend it overanything else because it is straighforward, clear and focused.Master itthen go on to Walter Rudin's Real and Complex Analysis. ... Read more

Book Description
This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure.

Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales.

This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory. ... Read more

Book 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

Book 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

Book 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

Book 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

Book 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· provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals · contains extended discussions on the four basic results of Banach spaces · presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties · details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions · covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theoryMeasure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines. ... Read more

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

Book 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

Customer Reviews (1)

Good for Review
Like the other books of the Schaum's Outline series, this book goes through the theories and shows you how to work the problems step by step.Although this is very helpful, I like to be able to test my knowledge.I say this is good for review because you will remember as you read this.You will also have a good idea of whether you are doing the supplementary problems correct or not.Here, most the supplementary problems do not have answers.Those that do, just have the final answer rather than an illustration of how the writers got the answer.This is difficult if you are learning about real variables for the first time.

As well as giving you the basic concepts, this book also goes into Lebesgue integrals, Riemann integrals, and Fourier series.The explanations are fairly well written, and the examples are easy to follow. ... Read more

Book Description
This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral. ... Read more

Book 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 (12)

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.

Very good introduction to measure theory
Very good intro for first encounters with measure theory. Throughout the application in probability theory is emphasized. The necessity of each concept introduced is motivated with clear examples. Interesting problem sets are provided after each section; their solutions are given in the appendix.

good book
This a good book but will be a bit difficult for engineering graduateslike me.. Should know real analysis and set theory to venture into this one.

clear introduction to measury theory
very clear measury theory introduction....with many detail solution to exercise....not bad !! ... Read more

Book Description
This book aims at restructuring some fundamentals in measure and integration theory and thus to free the theory from notorious drawbacks. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond. Thus it extends the Riesz representation theorem in terms of Radon measures from locally compact to arbitrary Hausdorff topological spaces. ... Read more

Customer Reviews (1)

Save your money for another book
For starters, this book uses non-standard notations or standard notations with non-standard meaning, which is annoying. For example, the bold capital letter I is used to denote of set of integers (rather than the standard Z). The standard blackboard bold letter N is used for the set of natural numbers, but the author excludes zero from that set (the author actually never defines N but it's apparent that zero is excluded from the given examples.) There are also quite a few typos (to cite just one example on page 20: "In the binary system every natural number x can be uniquely represented by x=sum from n=1 to infinity of x_n / 2^(n-1), where x_n is either 0 or 1."), but I gave up on the book when it claimed that the continuum hypothesis (the question of whether there exists a cardinal number strictly between the cardinality of the integers and the cardinality of the real numbers) was still an unsolved problem! ("This problem is yet unsolved").

For some strange reason, the author also develops the theory of cardinal numbers, which is only very marginally relevant to Lebesgue measure and integration. Sure, it's an interesting topic, but it really distracts from the main topic, and does not really belong in such a book.

The book has some redeeming features. In Appendix III, it has the English translation of Henri Lebesgue's lecture called "The Development of the Notion of the Integral" (reproduced from the book "Lebesgue Integration", by Soo Bong Chae, Marcel Dekker, New York, No. 58 (1980)). This lecture is a masterpiece.

It is also written in an accessible manner with good examples, definitions and theorems clearly stated, and instructive discussions, and a fair number of exercises.

However, these positive qualities are more than offset by the aforementioned flaws.
... Read more