Real Analysis and Probability

Cambridge Studies in Advanced Mathematics #74

by R.M. Dudley

Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.

Genres: Mathematics, Textbooks

450 pages, Hardcover

First published January 1, 1989

Reviews

[Tinwerume · Rating 4 out of 5]

I'm using this as a reference book for my research / companion to Kallenberg's Foundations of Modern Probability. I find it very readable while still covering the core of advanced probability theory very well.

I can't speak to how it would work as a book for someone trying to learn probability/real analysis for the first time though, and of course it's not as comprehensive as Kallenberg.

[William Schram · Rating 4 out of 5]

Real Analysis and Probability by R. M. Dudley is a textbook. Before I opened the book, I assumed it covered the real numbers instead of ones on the complex plane, but your guess is as good as mine. Around eight chapters in, it covers probability.

The book is a ceaseless line of proofs and theorems. Dudley makes it clear and concise, which is all you need in a mathematical text. The ideas are slightly more complicated than what I can handle. The book says it is a graduate-level text, so after college, I take it. However, the book has problems that you can solve as well.

Cambridge published the volume. It is the seventy-fourth in a series. Each chapter has a set of notes elaborating on what the author discussed. Finally, the end of each chapter contains a reference for further reading.

I enjoyed the book. Thanks for reading my review, and see you next time.