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Real Analysis and Probability

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Title: Real Analysis and Probability
by R. M. Dudley
ISBN: 0-521-00754-2
Publisher: Cambridge University Press
Pub. Date: 15 August, 2002
Format: Paperback
Volumes: 1
List Price(USD): $47.00
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Average Customer Rating: 4 (3 reviews)

Customer Reviews

Rating: 5
Summary: Fun for those who like abstract math
Comment: 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

Rating: 2
Summary: Not a good book for learning new material!
Comment: 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 condensed for studying analysis. Based on what the author presents, the problems are generally difficult to solve.

Rating: 5
Summary: Back in Print!
Comment: 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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