Supplementary reading for probability theory studies

Question

Can you advise some good books covering areas which are required for serious probability theory studies (e.g. measure theory, functional analysis)? Preferably this book should have some problem sets to work on. Thanks!

Answer 1

Take a look at "Measure Theory and Probability" by A.K. Basu. This book has lots of problem sets in them and contains some serious probabilty theory. It developed measure theory with probability as the main application. Also through-out the book there are examples which were really helpful.

Answer 2

For a broad overview in one book at a graduate level, it is hard to beat Foundations of Modern Probability (Second edition) by Olav Kallenberg. His presentation is classroom tested, and many standard complicated proofs have been made very concise. I'm a big fan of this book!

Answer 3

Pollard, A User's Guide to Measure Theoretic Probability

Answer 4

Dudley, Real Analysis and Probability

Answer 5

Billingsley, Probability and Measure.

Answer 6

A quite new and german one: Klenke, Wahrscheinlichkeitstheorie.

Answer 7

Jacod and protter is great.

Probability Theory: A Comprehensive Course by Klenke is worth looking at too.