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1. A Primer of Real Analytic Functions,
2. A Primer of Real Functions (Mathematical
3. Outsourcing the Sales Function:
4. Theory of Functions of a Real
5. The Theory of Functions of Real
6. Rational Approximation of Real
7. Differentiation of Real Functions
8. A Primer of Real Functions
9. Real and Abstract Analysis (Graduate
10. Scenes from the History of Real
11. Real Mathematical Analysis (Undergraduate
12. Real and Functional Analysis (Graduate
13. Principles of Real Analysis, Third
14. A Course in Calculus and Real
15. Singular Integrals and Differentiability
16. Lectures On The Theory Of Functions
17. Real Functions (Lecture Notes
18. A Handbook of Real Variables:
19. The elements of the theory of
20. The Elements of the Theory of

1. A Primer of Real Analytic Functions, Second Edition
by Steven G. Krantz, Harold R. Parks
Hardcover: 224 Pages (2002-06-27)
list price: US$99.00 -- used & new: US$68.99
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Asin: 0817642641
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Editorial Review

Product Description
The subject of real analytic functions is one of the oldest in modern mathematics and is the wellspring of the theory of analysis, both real and complex. To date, there is no comprehensive book on the subject, yet the tools of the theory are widely used by mathematicians today.

Key topics in the theory of real analytic functions that are covered in this text and are rather difficult to pry out of the literature include: the real analytic implicit function theorem, resolution of singularities, the FBI transform, semi-analytic sets, Faà di Bruno's formula and its applications, zero sets of real analytic functions, Lojaciewicz's theorem, Puiseaux's theorem.

New to this second edition are such topics as:* A more revised and comprehensive treatment of the Faà di Bruno formula * An alternative treatment of the implicit function theorem * Topologies on the space of real analytic functions * The Weierstrass Preparation Theorem

This well organized and clearly written advanced textbook introduces students to real analytic functions of one or more real variables in a systematic fashion. The first part focuses on elementary properties and classical topics and the second part is devoted to more difficult topics. Many historical remarks, examples, references and an excellent index should encourage student and researcher alike to further study this valuable and exciting theory. ... Read more

2. A Primer of Real Functions (Mathematical Association of America Textbooks)
by Ralph P. Boas
Hardcover: 319 Pages (1997-01-30)
list price: US$49.95 -- used & new: US$35.00
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Asin: 088385029X
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

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This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhere-oscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days. ... Read more

Customer Reviews (2)

5-0 out of 5 stars Great on Cantor's middle third set
Boas adds humor and curious anecdotes to his presentation of real functions.His book includes Lebesque integration and gives an excellent presentation of the Cantor set.

5-0 out of 5 stars A "must have" book if you love real analysis.
I've always enjoyed Ralph Boas' mathematical writing style. He is at his best in this small book. He covers topics in introductory and intermediate real analysis of one variable, but with an enthusiasm that pulls you along, like a good novel.This does not mean, however, that Boas skimps on theory and proof.This is an excellent resource for undergraduate/graduate study.The "Notes" section is a cornucopia of references to advanced topics by leaders in the field.And every exercise is answered, or at least addressed.
... Read more

3. Outsourcing the Sales Function: The Real Costs of Field Sales
by Erin Anderson, Bob Trinkle
Hardcover: 224 Pages (2005-02-10)
list price: US$50.95 -- used & new: US$21.99
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Asin: 0324207484
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description
This book sheds new light on the personal selling function in business-to-business markets. Well versed in the area of manufacturers' reps, the authors equip managers with the tools to determine the true costs and benefits of both in-house and outsourced forces. They explain in detail the differences between manufacturers' reps and company owned, tips for when to use them, how to most effectively work with them to optimize company return, and how to build strategic long-term alliances. The authors offer detailed information about the true costs and benefits of running a sales force and discuss how to effectively work with manufacturers' representatives to optimize your return. The book includes a CD-ROM with a cost calculator. ... Read more

Customer Reviews (5)

5-0 out of 5 stars Outsourcing The Sales Function
As a former product design engineer, I learned a good manufacturers' representative is worth his weight in gold.The rep is the person you turn to if you have component selection or vendor problems.Likewise, a good rep is a conduit for the voice of the customer; the person who makes clear the needs, the wants, and the opinions of the customer. Both roles are essential to a successful product design effort and both are difficult to fill.Like other positions that demand specific knowledge and experience, the job of a sales representative is a job for an specialist.

In "Out-Sourcingthe Sales Function", Anderson and Trinkle,- both experts on the topic- explain the intricacies of field sales show how, in many situations, an external sales force can outperform a traditional direct sales team. They give direct specific examples and show how the cost of the sales function can be accounted for accurately.Anyone who's livelihood depends directly or indirectly upon sales, will find this book revealing and useful.Highly recommended.

Bruce Long PhD, PE

5-0 out of 5 stars New Tool Aids Decision-Making about Outsourcing
These comments by Chicago PR consultant Laurence Kaufman, excerpted from a longer review, are right on the money.

Clearly directed at corporate executives with the responsibility for determining how their companies' goods are brought to market - CEOs and CFOs as well as their top sales executives - this book equally deserves careful scrutiny by manufacturers' representatives and their organizations, and by those who interface regularly with field sales people, i.e., distributors and other resellers, commercial and industrial end users.

A number of factors make this book noteworthy, but perhaps the most important is its authorship - a unique collaboration between an academic (Erin Anderson) who has been studying manufacturers' representatives and the decision to employ them for a quarter-century and a field sales professional (Bob Trinkle) who spent close to half a century practicing what he now preaches. And what Trinkle preaches, along with his professorial collaborator, is not that you should choose the rep route to market, but that you should make the choice intelligently - based not only on economic factors but also in full realization of the impact of corporate culture and product idiosyncrasies - and if you choose to outsource, the factors you need to consider in making the strategy work. Trinkle and Anderson do not say that outsourcing is the right thing to do - it may or may not be. But if you decide it is the right thing to do, they also tell you how to do it right.

Another noteworthy feature is the inclusion with the hard-cover book of a CD-ROM Cost Calculator©, that allows those responsible for making dollar comparisons between in-house and outsourced field sales to plug in their own numbers, reminding them along the way of the "soft costs" that go away in tandem with the decision to outsource.

Anderson and Trinkle have created a tool not only for making strategic decisions about how to take products into the field, but for creating a better understanding of the role of the rep as an advocate for buyers and for sellers. If you are a rep who wants to be thought of as an OSP (Outsourced Sales Professional), first read this book; and then make sure each of your principals reads it as well. If you are a customer or reseller, it will remind you of the benefits the OSP brings you in efficiency, advocacy, and continuity. If you are amanufacturer, it will help you analyze when to outsource, when to go or stay direct, and when to field a hybrid sales force, and prevent a decision from being made capriciously.

5-0 out of 5 stars Excellent -carefully written and thoroughly researched
This ranks as one of the best written books and a must have.I recommend this to anyone in marketing and sales, from entry level sales people to marketing and sales managers and even CEOs/CFOs.I have over 20 years in establishing new markets, recruiting and managing the sales force and this book is a treasure that I could have utilized throughout my career.Why learn by trial and error when you have so much knowledge in a book?It is apparent to me, that this book is written from "boots on the ground" real-life experience.Concepts are clearly presented and backed up by real world examples.The included CD is a remarkable utility allowing one to caculate true cost of sales and compare business models.Compare current busines practices to a benchmark.An independent sales representative could use this to negotiate commission rateson new contracts with principals.

5-0 out of 5 stars Excellent read on a great way to go to market !
Bob and Erin do an excellent job of frameworking the decision criteria of when to use outsourced sales professionals. Reviews the tough topic of the true costs associated with using OSP's vs. direct sales. This is the best book I have seen on this subject. If you are looking at your cost of goods sold and not currently using manufacturer's representatives, this book might give you insight into a great way to go to market !

4-0 out of 5 stars A Good Read!
Outsourcing has become an accepted business practice because it can deliver demonstrable savings and improved services. However, while sales outsourcing is common, it has not been widely adopted by companies accustomed to having dedicated in-house sales staffs. Authors Erin Anderson and Bob Trinkle make a powerful case for the benefits of using outside sales reps, asserting that they cost less and sell more, particularly when they use the tactic of "portfolio selling." The authors explain how the two types of sales forces can co-exist and augment each other. Die-hard sales managers will find interesting material here, though the book belabors a few obvious points and lacks enough real-world examples to juice up the dry text. The authors include a CD with software for analyzing sales costs. Since this is a very specific book for anyone investigating whether to use reps, we recommend it to sales directors and executives who are facing that question. However, front line salespeople and reps should just keep to their appointment books - this text is not designed for you. ... Read more

4. Theory of Functions of a Real Variable 3RD Editio
by E W Hobson
 Paperback: Pages (1927-01-01)

Asin: B003OTM7X2
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5. The Theory of Functions of Real Variables: Second Edition (Dover Books on Mathematics)
by Lawrence M Graves
Paperback: 400 Pages (2009-11-18)
list price: US$16.95 -- used & new: US$10.00
(price subject to change: see help)
Asin: 0486474348
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Editorial Review

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The theory of functions of real variables constitutes a pillar of modern mathematical analysis. This balanced introductory treatment covers all of the fundamentals, from the real number system and point sets to set theory and metric spaces. Useful, well-chosen lists of references to the literature conclude each chapter. 1956 edition.
... Read more

6. Rational Approximation of Real Functions (Encyclopedia of Mathematics and its Applications)
by P. P. Petrushev, Vasil Atanasov Popov
 Hardcover: 384 Pages (1988-04-29)
list price: US$110.00 -- used & new: US$110.00
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Asin: 0521331072
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Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in the mid-sixties. The authors aim at presenting the basic achievements of the subject and, for completeness, also discuss some topics from complex rational approximation. Certain classical and modern results from linear approximation theory and spline approximation are also included for comparative purposes. This book will be of value to anyone with an interest in approximation theory and numerical analysis. ... Read more

7. Differentiation of Real Functions (Crm Monograph Series)
by Andrew Bruckner
Hardcover: 195 Pages (1994-05-05)
list price: US$62.00 -- used & new: US$56.48
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Asin: 0821869906
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Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an efficient account of the present state of the subject. Bruckner addresses in detail the problems that arise when dealing with the class $\Delta '$ of derivatives, a class that is difficult to handle for a number of reasons. Several generalized forms of differentiation have assumed importance in the solution of various problems. Some generalized derivatives are excellent substitutes for the ordinary derivative when the latter is not known to exist; others are not. Bruckner studies generalized derivatives and indicates ``geometric'' conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail. The book unifies many important results from the literature as well as some results not previously published. The first edition of this book, which was current through 1976, has been referenced by most researchers in this subject. This second edition contains a new chapter dealing with most of the important advances between 1976 and 1993. ... Read more

8. A Primer of Real Functions
by ralph boas
 Hardcover: 189 Pages (1960-01-01)

Asin: B0000CKOUB
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9. Real and Abstract Analysis (Graduate Texts in Mathematics) (v. 25)
by Edwin Hewitt, Karl Stromberg
Hardcover: 492 Pages (1975-05-20)
list price: US$89.95 -- used & new: US$49.95
(price subject to change: see help)
Asin: 0387901388
Average Customer Review: 5.0 out of 5 stars
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Customer Reviews (3)

5-0 out of 5 stars still one of the best
After 30 years of its first publications, this book remains one of the best. It treats all the elements of a graduate course in analysis thoroughly. One of the few books that actually goes through construction of the real number system (in Chapter 1) and products of infinitely many measure spaces (in Chapter 6). There is plenty material to choose from, and all the standard topics are covered. In a very few cases notation is a bit cumbersome (or obsolete), but this is no big problem. Highly recommended to all graduate students in mathematics.

5-0 out of 5 stars Excellent real analysis reference
In many applications today, such as PDE or harmonic analysis, it is crucial to have a really good grasp of the Lebesgue integral and absolutely continuous (rather than continuously differentiable) functions. Many real analysis books shy away from these matters.

Hewitt and Stromberg provide *every* detail, starting from scratch with measure theory, including Caratheodory's construction and fine distinctions such as Lebesgue vs. Lebesgue-Borel measurable sets. They proceed to discuss the Lebesgue integral in detail, then differentiation and absolutely continuous functions, the Lebesgue spaces including Riesz representation and a Banach space primer and finally integration on products (also infinite) of measure spaces. Fourier series and transforms are covered as well as fine details of (naive) set theory.

The book would be perfect if some standard analysis (Taylor series, analytic functions, Hospital rule, ...) was discussed; for this reason and because of its high level, it cannot be recommended as a book for 1st year calculus.

5-0 out of 5 stars One of the best references on the subject
This is the kind of book I appreciate the most: one that's always got the information you need. This meticulous text covers thoroughly just every topic from elementary set theory up to product measures. It developscarefully all topics that should be included in standard analysis lectures(set theory, topology, Lebesgue integral, Banach and Hilbert spaces,differentiation, product measures) at such level of abstraction that thebook turns out to be suitable for introductory courses, advanced courses,and later reference. The only one shortcoming I see is that the bookincludes no bibliography.

Please check my other reviews at my member page(click on my name above). ... Read more

10. Scenes from the History of Real Functions (Science Networks Historical Studies, Vol 7)
by Fyodor A. Medvedev
 Hardcover: 268 Pages (1992-02-04)
list price: US$229.00 -- used & new: US$229.00
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Asin: 0817625720
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11. Real Mathematical Analysis (Undergraduate Texts in Mathematics)
by Charles C. Pugh
Paperback: 437 Pages (2010-11-02)
list price: US$69.95 -- used & new: US$56.00
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Asin: 144192941X
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises. ... Read more

Customer Reviews (12)

5-0 out of 5 stars One of the Best Books in Analysis, or even Maths
I dont know how to say how good this book is: it not only teaches us the technical aspects of mathematics, it also teaches us intuitions, ideas behind the proofs, styles, and philosophy.

I would like to also start with a comparison of the classic baby Rudin:

While Rudin's little book is also a real gem, I would say Pugh's belongs to a slightly higher level (due to its problems mainly and topic selection and coverage). Rudin's book could either be used in 1st year one semester as a strong first course in basic analysis (1st 7 chapters) for extremely motivated and hardworking students (such as those at MIT, Harvard, Princeton, and many other good institutions), or ought to be supplemented in an honour's undergrad real analysis (in 2nd year or 3rd year). Its presentation of Lebesgue theory is rather incomplete and no one virtually uses it for lebesgue theory. On the other hand, pugh has a full chapter on it, covering almost all the standard undergrad lebesgue materials.

Pugh's book on the other hand can be the last reading before attempting Folland and Big Rudin. Knowing pugh well and having solved its problems would make Folland and big Rudin not hard, whereas little rudin may not surve this purpose that well. Many Rudin's problems are hard but standard (Prove, Show this. Very few is it true? what about?), whereas Pugh's is more thought provoking (Is it true? What about? What do you think? which mimics a key part in maths research).

Moreover. mathematics is not just about formalism and logic, especially in analysis ang geometry. The ideas and our feeling about how the objects behave are at least equally important. (Anyone can write proofs well with sufficient training; yet not everyone feels that a measurable function is no more complicated than continuous ones in a sense; why lebesgue's definition of length and integral are powerful; weirstrass approximation is as simple as "taking expectations of functionals", etc.) Amazingly Pugh's book trains people to this direction very well.

1-0 out of 5 stars I prefer Bartle and Sherbert
I used this book in my first Real Analysis course and thoroughly disliked it.I seems that everyone else who reviews this book mentions Rudin.I haven't had a chance to read Rudin yet but I prefer Intro to Real Analysis by Robert G. Bartle and Donald R. Sherbert over this book.Many people like Pugh for it's conversational tone but I found it annoying.This might be a good secondary book but I wouldn't recommend this as your first book in real analysis.Pugh makes the cardinal mistake of mathematicians in introducing the most general case first.The most important thing in mathematics is not the most general case but the process of generalization itself.This is like saying the journey is as important as the destination.To generalize one must start with a specific case and then work, layer by layer, to the most general case.That's one reason I prefer Bartle and Sherbert.It starts with functionsfrom R to R and generalizes from there.It takes up where undergraduate calculus leaves off.I also prefer the exercises in Bartle and Sherbert better. They are challenging without being infuriating. They are still general proofing exercises but are specific enough to deal with specific functions, series, sequences, and so forth.I was also annoyed by the way Pugh qualifies his proofs like Chapter 1 Theorem 2: "Proof Easy" ,or theorem 9: "Proof Tricky!", or Chapter 2 Theorem 10:"Proof, Totally natural!".I feel his language is imprecise and sloppy. I feel the section on cuts is superfluous. It seems that cuts are a lot of work and headaches just to prove that everything I learned in elementary school is correct. I was worried that x+0 didn't really equal x but now with cuts, I can rest assured that it does! Whew, what a relief!The only plus to Pugh is the thorough chapter on metric spaces helps put things into a broader context.All and all I dislike Pugh's book and highly recommend Bartle and Sherbert. as the best introduction to Real Analysis.

5-0 out of 5 stars Excellent problems and diagrams -- great book
This is an excellent introductory text on real analysis. It is very approachable, and he does a very good job at supplementing the traditional "definition-theorem-proof" style with intuitive explanations and wonderfully descriptive diagrams (the diagrams are one of the strongest points of this book -- and are something that are sadly left out of many otherwise good books on analysis).

My only (minor) complaint is with the layout/formatting of the book -- it is very jumbled together, the typesetting is poor, and it looks like it was printed on a low-resolution $10 printer.

Other than that, it is an excellent companion to a more in-depth/advanced treatment. As far as more "advanced" books go, I would recommend -- Apostol's "Mathematical Analysis" and/or Shilov's "Real and Complex Analysis" -- both of which are incredibly well written and informative.

5-0 out of 5 stars Pugh is wonderful. Rudin is good too, but both texts working together is the best.
I wish that I had discovered Pugh in my first semester of undergraduate analysis. The assigned text was Rudin and it was a great choice. The exposition there is excellent. The exercises are incredibly well done. Pugh covers just about the same material as Rudin, and in the same rigor, but is more likely to give you paragraphs before and after important theorems/definitions that help to clarify things. I must admit I am not too familiar with the first half of Pugh's text as I didn't discover it until I was well in chapter 10 of Rudin ~~ chapter 5 of Pugh. But, if the first chapters are as good as the fourth and fifth, you can get just as much from Pugh as from Rudin, if not more.

Sometimes, you get a picture (this would have been really helpful back when I was learning what an open cover was). Other times, Pugh actually gives a better presentation. For instance, when discussion the rank theorem, Rudin's statement of it is hard to follow. The proof is about as difficult. Pugh, however, introduces C' equivalence and then gives an alternate statement of the theorem which is much more intuitive. AND some pictures after the proof. Some think having pictures in analysis books is bad--Pugh gives evidence otherwise.

It is difficult to say which text has better exercises as I have not attempted them all. But Pugh definitely has more of them. I think the best thing for any undergraduate to do is to just own both books. Rudin is the standard for a good reason. Pugh's or someone else's exposition may become the standard in the future, but Rudin will always be an excellent reference. Doing Rudin's exercises will help prepare you for your qualifying exams if you ever take them. Pugh has some UC Berkeley good prelim exam questions in his book which prepare you for future math endeavors as well. So I say just buy both. But if you can only buy one.... probably get Pugh because he's cheaper. Or you can get International Edition Rudin for cheaper still.

5-0 out of 5 stars Brilliant
The style is friendly and fun, and the presentation is really intuitive! My personal favorite! ... Read more

12. Real and Functional Analysis (Graduate Texts in Mathematics) (v. 142)
by Serge Lang
Hardcover: 600 Pages (1993-04-29)
list price: US$74.95 -- used & new: US$56.13
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Asin: 0387940014
Average Customer Review: 4.5 out of 5 stars
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This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters. ... Read more

Customer Reviews (3)

5-0 out of 5 stars One of a kind !
Up to my knowledge, this is the only book that constructs the Lebesgue integral for functions to a general Banach-space instead of the real numbers (thus saving us from the unnecessary and esthetically dissapointing construction through positive and negative functions).
I don't know how Lang does it, but eerytime you'll pick up one of his books, you'll marvel at the beauty of mathematics !

5-0 out of 5 stars Much better than Royden!
It drove me up the wall, in my first course on measure and integration, that integration was first done for positive functions, then for real functions by writing them as a difference of positive functions, then complex functions in terms of real and imaginary parts.Why couldn't you just integrate real-valued functions
intrinsically, without the silly decomposition into positive and negative parts?

After that course, I found Lang's book.What a blessing to see that you can just integrate in infinite-dimensional spaces right from the start.I can't understand why virtually all books on integration theory still succumb to the "positive functions first" approach.

4-0 out of 5 stars Overall, A Good Book
I've read several analysis books and this is one of the better ones that I have read.It covers a variety of interesting and useful topics and the exposition is clear. It's presentation is a bit more abstract than some others starting with some functional-analytic concepts before doing integration in that framework. However, if you want to study stochastic analysis, getting in this frame of mind will definitely help your understanding of stochastic integration. For a truly thorough understaning of the subject, I recommend purchasing this book as well as the somewhat easier "Lebesgue Integration on Euclidean Space" by Frank Jones - the two together cost about the same as Royden, Rudin, or the terrible book by Aliprantis. ... Read more

13. Principles of Real Analysis, Third Edition
by Charalambos D. Aliprantis
Hardcover: 415 Pages (1998-09-09)
list price: US$141.00 -- used & new: US$59.95
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Asin: 0120502577
Average Customer Review: 4.0 out of 5 stars
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With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians ... Read more

Customer Reviews (4)

5-0 out of 5 stars A Welcome Addition to the Perplexing World of Real Analysis
Again, thirty or forty years ago you wouldn't have found a book like this one for the subject of Real Analysis. First off the authors offer an answer book for the problems given in the text. In the "old days" this just wasn't done. Something about: "you have to suffer to obtain glory" was what one of my Math professors often said. Oh yeah it was:" there is no royal road to learning mathematics". That was his line.

Well things change. And now these authors for what ever reason have tried to give us poor "challenged types" a break. Good for them!

Usually the complaints about the subject of Real Analysis and its teaching are of a particular or specific type. Like; "I don't get it!". That's usually the nature of the "whining and crying".

Probably the crime originates notin University courses so much as it originates in High School Mathematics teaching. That is the High School
Mathematics teacher who takes his/her frustrations out on the class.
That is where the student first hears the word, "Real Number".

"Yeah", they often say "...whad'ya mean by Real? It's a number ain't it?
It's gotta be real!" end of quote. I never ever had a Math teacher in HighSchool prove the irrationality of the square root of two. First off that's a proof by contradiction. Yet the Ancient Greeks showed it to be so 2500 years ago. But somehow it never got done in my High School when I was there. Also "Countability". Nevergot done in myHigh School.

So that by the time you get to University and they throw Cantor's proof for the non-denumerability of the Real numbers at you, you often feel a weird sensation of having been "defiled", somehow "violated". Violated because you really were never taught how to count 1,2,3,...properly.And since an irrational number like the root of two is uncountable you can't go "1, 2, 3,...." pointing at it with your finger. Since you can't point at it with your finger it " really doesn't really exist " as we human beings "know" existence. We know it exists but we can't "point to it".
That was what they couldn't get across in High School or even University.

What they tried to teach us in High School Algebra of course was factoring. Okay. But then they couldn't teach us the Binomial Theorem because they, the teachers didn't know it themselves. There's that word "know". And then if you did show some desire to learn more they got angry and said: " ...this is way, way above your head!". Whose head?
There's or mine?

Now I study Real analysis on my own. Certainly not for any monetary profit. I'm what you call an "amateur"...for the "love". This book is an invaluable aid to that end.

Best Regards

Southern Jameson West

5-0 out of 5 stars Excellent Coverage plus a wealth of problems
Finished reading those undergraduate analysis books that made a study of metric spaces look like a tall order? Well then reading this book would be an excellent continuation of the hard work. The book is largely about the Lebesgue theory of integration, but includes a very thorough coverage of the theory of metric and topological spaces in the first two chapters. Chapters 3,4 and 5 are the heart of the book covering measure theory, the Lebesgue integral and some topics from introductory functional analysis like theory of operators and Banach spaces. Chapters 6 and 7, covering Hibert spaces, the Radon Nikodym theorem and the Riesz Representation Theorem among other things, are the most useful for someone like me who wants to master higher analysis in order to read financial mathematics. And what's more, there is a solutions book providing answers to all 609 problems (spread over 7 chapters!) and more. All in all, the authors have made a great contribution!

2-0 out of 5 stars Very Mediocre Contents, Terrible Aesthetics
I was very disappointed in this book and judging from the steady decline of the resale price here on amazon.com, I can see others agree.

First of all the book looks like it was photocopied in someone's basement - the text is completely faded out and paper feels terrible. For almost $100, I expect a little more.

The actual contents of the book are not much better. I found Royden (the required text for our class) to be very sparse and was hoping for something to fill in the details. This book did little to help. It covers integration in a rather idiosyncratic way, devotes little time to differentiation, and says nothing about convexity.

If you are looking for a good anaysis book I recommend either "Lebesgue Integration on Euclidean Space" by Frank Jones or the slightly more abstract "Real and Functional Analysis" by Serge Lange

5-0 out of 5 stars One of the best
An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text. ... Read more

14. A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)
by Sudhir R. Ghorpade, Balmohan V. Limaye
Paperback: 432 Pages (2010-11-02)
list price: US$69.95 -- used & new: US$52.45
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Asin: 1441921451
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Editorial Review

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This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

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15. Singular Integrals and Differentiability Properties of Functions. (PMS-30)
by Elias M. Stein
Hardcover: 304 Pages (1971-02-01)
list price: US$94.00 -- used & new: US$63.45
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Asin: 0691080798
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

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Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself.

Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance.

Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.

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Customer Reviews (1)

5-0 out of 5 stars Must-have advanced text on harmonic analysis.
This appreciated book constitutes since its first printing one of the finest references on advanced harmonic analysis and some related topics. The author, one of the leading experts in the field, exposes clearly mostof the general background as well as recent results, orienting the readerdirectly to the current trends in research.

The book is valuable not onlyfor harmonic analysis speciallists, but for every mathematician who wantsto get well trained in some important and subtle topics of analysis whichare shown by this approach as being closely related, leading the reader toa deep and thorough understanding.

The contents of the book are: Somefundamental notions of real-variable theory; Singular integrals; Riesztransforms, Poisson integrals, and spherical harmonics; TheLittlewood-Paley theory and multipliers; Differentiability properties interms of function spaces; Extensions and restrictions; Return to the theoryof harmonic functions; Differentiation of functions; Appendices: Someinequalities; The Marcinkiewicz interpolation theorem; Some elementaryproperties of harmonic functions; inequalities for Rademacherfunctions.

Includes motivation and detailed explanations for each topic,excercises for each chapter, called "further results", which aresmall research projects on their own, and extensive references. Theprinting and the clothbound are exquisite.

This kind of material shouldbe included in every graduate mathematics program. Should read companion"Introduction to Fourier Analysis on Euclidean Spaces" (anotherjewel) by Stein and Weiss, and later the recent volume "HarmonicAnalysis" also by Stein, both reviewed by myself.

Please take a lookat the rest of my reviews (just click on my name above). ... Read more

16. Lectures On The Theory Of Functions Of Real Variables V2 (1912)
by James Pierpont
Hardcover: 660 Pages (2008-06-02)
list price: US$63.95 -- used & new: US$44.12
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Asin: 1436573602
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This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

17. Real Functions (Lecture Notes in Mathematics)
by Brian S. Thomson
Paperback: 240 Pages (1985-12-20)
list price: US$46.00 -- used & new: US$46.00
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Asin: 3540160582
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18. A Handbook of Real Variables: With Applications to Differential Equations and Fourier Analysis
by Steven G. Krantz
Hardcover: 201 Pages (2003-11-18)
list price: US$69.95 -- used & new: US$11.05
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Asin: 081764329X
Average Customer Review: 2.0 out of 5 stars
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This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter.

Key features:

* Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students

* Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis

* Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use

* Illuminating applications of many theorems, along with specific how-to hints and suggestions

* Extensive bibliography and index

This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for applied mathematicians, physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, "A Handbook of Real Variables" will benefit a wide audience. ... Read more

Customer Reviews (1)

2-0 out of 5 stars I Kinda Wish I Had Not Bought This
Don't get me wrong - Krantz is good but this is essentially Baby Rudin - without the proofs - which is sort of like a bar without beer. ... Read more

19. The elements of the theory of real functions
by John E Littlewood
 Paperback: 71 Pages (1954)

Asin: B0007DO5J2
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20. The Elements of the Theory of Real Functions; Being Notes of Lectures Delivered in the University of Cambridge
by j littlewood
 Hardcover: Pages (1956)

Asin: B0043TT6NG
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