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Real Analysis and Probability (Paperback)

~ (Author) "In constructing a building, the builders may well use different techniques and materials to lay the foundation than they use in the rest of the..." (more)
Key Phrases: image measure theorem, maximal ergodic lemma, isonormal process, New York, Theorem Let, Amer Math (more...)
4.2 out of 5 stars  See all reviews (10 customer reviews)
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Editorial Reviews

Review

"A marvelous work which will soon become a standard text in the field for both teaching and reference...a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs througout the text. Some of the topics and proofs are rarely found in other textbooks." Proceedings of the Edinburgh Mathematical Society


Product Description

This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.
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Product Details

  • Paperback: 566 pages
  • Publisher: Cambridge University Press; 2nd edition (August 15, 2002)
  • Language: English
  • ISBN-10: 0521007542
  • ISBN-13: 978-0521007542
  • Product Dimensions: 8.8 x 6 x 1.5 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon.com Sales Rank: #503,367 in Books (See Bestsellers in Books)

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More About the Author

R. M. Dudley
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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Inside This Book (learn more)
First Sentence:
In constructing a building, the builders may well use different techniques and materials to lay the foundation than they use in the rest of the building. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
image measure theorem, maximal ergodic lemma, isonormal process, closed regularity, independent real random variables, measurable cover, portmanteau theorem, regularity extension, reversed martingale, sample continuity, separable metric space, interval topology, support hyperplane, regular conditional probabilities, pseudometric space, martingale sequence, countably additive measure, product topology, countable product, inner measure, finite measure space, continuous real functions, finite subcover, lim infra, analytic sets
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Theorem Let, Amer Math, Comptes Rendus Acad, Uspekhi Mat, Proof Let, Proposition Let, Russian Math, Academic Press, Dictionary of Scientific Biography, Lemma Let, Exact Sci, Andrei Nikolaevich, Acta Math, Proposition There, Van Nostrand, Circolo Mat, Danske Vid, London Math, Probability Appls, Studia Math, Theorem Every, Theorem Given, Zur Theorie, Atti Accad
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Citations (learn more)
This book cites 71 books:
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100 books cite this book:
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Stone Spaces by P. T. Johnstone
 

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Customer Reviews

10 Reviews
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Average Customer Review
4.2 out of 5 stars (10 customer reviews)
 
 
 
 
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Most Helpful Customer Reviews

 
28 of 29 people found the following review helpful:
5.0 out of 5 stars A classic text in theoretical probability, January 27, 2005
By Thomas L. Ritchie (São Paulo, Brazil) - See all my reviews
(REAL NAME)   
First of all I should say that this book was written for those interested in the foudations of probability theory (the same is also true for Prof. Kallenberg's book). Therefore beginners learning real analysis and probability for the first time and those looking for applications should look elsewhere to find out appropriate books (instead of underrating such an important text like Prof. Dudley's book).
The second point to be emphasized is that this book fills in an important gap in probability literature as it reveals numerous links between this branch of mathematics and other areas of pure mathematics such as topology, functional analysis and, of course, measure and integration theory, while most books on advanced probability develop barely the latter connection, which is plainly insufficient for (future) researches on probability theory.
Finally, despite the complaint of some reviewers, the book is extremely well written and amazingly comprehensive. The sole prerequisite to reading it is a certain amount of "mathematical maturity" which perhaps these reviewers lack.
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27 of 29 people found the following review helpful:
5.0 out of 5 stars Fun for those who like abstract math, September 10, 2003
By A Customer
You will find this an excellent book, as long as you belong to its target public. The book is targeted towards real mathematicians interested in a very theoretical approach of probability and the underlying real analysis framework. Although this book is very much self contained (in principle you do not need any pre-knowledge of real analysis since everything is explained from the beginning), the reader should have a rather high level of maturity in abstract math. It is definitely not a book for beginners, since it has a high level of abstraction. If you only want to learn the more practical 'calculus alike' aspects based on intuition, you should buy another book. On the other hand, if you like highly theoretical and abstract math, if you want rigor,if you are a mathematical researcher,... this book deserves a closer look.
Readers of books at this level will definitely need to invest more time than with the average math books, but will be rewarded with the indescribable feeling of understanding the creative thoughts of some great mathematicians.

Key points are :
-explains everything you need from zero. The first chapter for instance starts with basic set theory, subsequent chapters
describe basic topology, Hilbert an Banach spaces and functional analysis. Further chapters then move to probability based on the theoretical underpinning of the first half of the book.
-contains not always the most intuitive proofs, but definitely the most beautiful, creative and elegant ones.
-contains interesting notes and historical aspects at the end of each chapter.
-does not cheat on the proofs : there are no gaps in the proofs that are left as an exercise to the reader. Everything is explained in full detail.
-is up to date with the most recent theoretical developments.

If you like abstract math, give it a try and enjoy

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11 of 11 people found the following review helpful:
5.0 out of 5 stars Back in Print!, October 14, 2000
By A Customer
This review is from: Real Analysis and Probability (Wadsworth & Brooks/Cole Mathematics Series) (Hardcover)
This book was out of print for a few years, but Cambridge Univ Press has issued a revised edition. This is my favorite book for real analysis, measure theory, and probability theory. The book is very self-contained and rigorous, and develops probability theory abstractly enough for advanced work in the field. If you are interested in empirical process theory, this text can be followed by Dudley's book on Uniform Central Limit Theorems.
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Most Recent Customer Reviews

5.0 out of 5 stars Older edition, better clarity
The book is almost identical in the content to the later published Cambridge University Press copy, except for omission of the Stone-Weierstrass theorem. Read more
Published 10 months ago by jmathb

3.0 out of 5 stars A great book but not as a textbook for real analysis
I have been teaching a one semester course of Real Analysis (measure and integration) from this book. Read more
Published 11 months ago by Traveler

5.0 out of 5 stars masterpiece
This is a great book. The mathematical exposition is excellent and the historical footnotes are extremely interesting.
Published on August 31, 2006 by Daniel Tancredi

5.0 out of 5 stars A classic
This is absolutely a classic book on real analysis and probability, although it is a little hard to read. Read more
Published on October 5, 2004 by Machine will be able to learn

2.0 out of 5 stars Yakkkkkkkkkkkk............
This is a text book for math major students. I believe nothing is more terrible than a book full of theorems without adequat samples. And this happen to be one. Read more
Published on September 22, 2004 by Ian TX

5.0 out of 5 stars one of the best
This is one of the best textbooks on real analysis and probability (at the graduate level). You will need a solid undergraduate course in analysis before being able to read this... Read more
Published on July 14, 2004

2.0 out of 5 stars Not a good book for learning new material!
This is definitely not a good book for learning the material for the first (or even second!) time. It's difficult to read, has too few examples, and the material is way too... Read more
Published on August 28, 2003

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