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Real Analysis and Probability | 
 enlarge | Author: R. M. Dudley
Publisher: Cambridge University Press
Category: Book
List Price: $62.00
Buy New: $51.62
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Rating:  8 reviews
Sales Rank: 482088
Media: Paperback
Edition: 2nd
Pages: 566
Number Of Items: 1
Shipping Weight (lbs): 1.7
Dimensions (in): 8.8 x 6 x 1.5
ISBN: 0521007542
Dewey Decimal Number: 515
EAN: 9780521007542
Publication Date: August 15, 2002
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Shipping: International shipping available
Condition: Brand new item. Over 4 million customers served. Order now. Selling online since 1995. Few left in stock - order soon. Code: C20080923192238B
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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.
Book Description
This classic graduate textbook, now reissued in paperback, 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 excercises have been added, together with hints for solution.
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| Customer Reviews: Read 3 more reviews...
 A classic text in theoretical probability January 28, 2005
Thomas L. Ritchie (Sao Paulo, Brazil)
28 out of 29 found this review helpful
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.
Fun for those who like abstract math September 10, 2003
26 out of 27 found this review helpful
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
masterpiece August 31, 2006
Daniel Tancredi (Davis, CA)
4 out of 5 found this review helpful
This is a great book. The mathematical exposition is excellent and the historical footnotes are extremely interesting.
A classic October 5, 2004
Machine will be able to learn (USA)
10 out of 12 found this review helpful
This is absolutely a classic book on real analysis and probability, although it is a little hard to read. Highly recommend to people working in machine learning and/or pattern recognition, since it provides almost all mathematical foundations needed to do deep research in these two fields, for example, on statistical learning theory.
Back in Print! October 14, 2000
10 out of 10 found this review helpful
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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