Real Analysis and Probability (Cambridge Studies in Advanced Mathematics, Series Number 74)

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.

Simply superb, you will fall in love with this book. Probably not the best for a first or 'quick' reading, but if you persevere, you will reap the rewards. The more you read, the more you appreciate what this book has. Specially, the historical notes at the end of each chapter are priceless. Great stuff from Professor Dudley.

I had the older copy many years ago. The second edition is even better and with paperback. This book builds better connection between real analysis and probability than the earlier Robert Ash's text. It's a good reference for anyone who is interested in having some foundations for theoretical probability.

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.

This is a great book. The mathematical exposition is excellent and the historical footnotes are extremely interesting.

I have been teaching a one semester course of Real Analysis (measure and integration) from this book. The students have already been through a course based on Rudin's Principles of Mathematical Analysis though not the Lebesgue integral there, and pretty comfortable with metric spaces and such and the standards of mathematical proof. So as the next step in analysis this book seems to be in the right place esp. because the book advertises itself as self-contained.While I appreciate the wonderful integration of Real Analysis and Probability and short proofs, the brevity is often achieved by omitting details rather than choosing a simpler argument and so the book is a bit too hard on the students. Many proofs are too terse and have significant gaps which often take a lot of classroom time to get over, unless you are willing to leave them puzzled. The wording in the proofs is often counterintuitive, in particular it is usually not clear if the sentence continues the line of argument or starts a new one. This is an unnecessary hiccup for the reader and it would cost just few friendly words here and there to fix. Overall the book is harder to follow than Royden's Real Analysis. Many of the exercises are great and illuminative but many are just impossibly hard.

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. The "A Probability Path" is much better than this one.