TITLE: Good books on "advanced" probabilities
QUESTION [46 upvotes]: what are some good books on probabilities  and measure theory?
I already know basic probabalities, but I'm interested in sigma-algrebas, filtrations, stopping times etc, with possibly examples of "real life" situations where they would be used
thanks

REPLY [5 votes]: I really like
Probability with Martingales by D. Williams  and Probability: Theory and Examples by Durrett.