TITLE: Supplementary reading for probability theory studies
QUESTION [5 upvotes]: 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!

REPLY [2 votes]: Jacod and protter is great.
Probability Theory: A Comprehensive Course by Klenke is worth looking at too.