Principles of Real Analysis 3rd Edition by Charalambos D. Aliprantis (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student.” –J. Lorenz in ZENTRALBLATT FUR MATEMATIK”A clear and precise treatment of the subject. All details are given in the text…I used a portion of the book on extension of measures and product measures in a graduate course in real analysis. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use.” –CASPAR GOFFMAN, Department of Mathematics, Purdue University From the Back Cover The new, Third Edition of this successful text covers the basic theory of integration in a clear, well-organized manner. The authors present an imaginative and highly practical synthesis of the “Daniell method” and the measure theoretic approach. It is the ideal text for undergraduate and first-year graduate courses in real analysis.This edition offers a new chapter on Hilbert Spaces and integrates over 150 new exercises. New and varied examples are included for each chapter. Students will be challenged by the more than 600 exercises. Topics are treated rigorously, illustrated by examples, and offer a clear connection between real and functional analysis.This text can be used in combination with the authors’ Problems in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text.@introbul:Key Features:@bul:* 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@qu:”All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student.”@source:–J. Lorenz in Zentralblatt für Mathematik@qu:”…a clear and precise treatment of the subject. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use.”@source:–CASPAR GOFFMAN, Department of Mathematics, Purdue University

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 not in University courses so much as it originates in High School Mathematics teaching. That is the High SchoolMathematics 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 High School 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”. Never got done in my High 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 RegardsSouthern Jameson West

⭐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

⭐The book itself is good, but the binding sucks! After the first week the binding is coming apart, now the book has all these loose pages.

⭐The descriptions are clear to me. Sometimes it is a bit compact, but with some serious attention, good to follow.

⭐Pros:1,In a separate book the authors provide all the answers. It is extremely helpful for students learning Lebesque integration for the first time and those who are self studying the subject.2,Good organization. The authors have a good habit to list all the useful properties together right after they introduced a concept, so the book is good for reference.Cons:1,Many proofs are long winded. Compare the proofs of monotone and dominated convergence theorem to those of Rudin’s and you will find the latter to be more concise AND easier to understand.2,Many unnecessary treatments. Check the definition of simple function to see what I mean. The authors also use semiring instead of sigma-algebra, which is both unnecessary and annoying, at least to me.Conclusion:I give a 4 star rating because only a handful of textbooks at this level provide solutions to all the problems. But I find this book to be boring to read. Seriously, at least half dozen books on this subject have better exposition than this one.

⭐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!

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