TITLE: A Good Book for Mathematical Probability Theory
QUESTION [8 upvotes]: I am from mathematical background, and I always hated the way they teach elementary probability theory in schools without giving any clue about measure theory. 
I want a theoretical book in probability theory, which starts with measure theory
and defines everything in mathematical terms. I am also not looking for a measure 
theory book. If there is such a book that instead of giving only an intuitive introduction
to probability theory, it rather defines everything in details, I would be really grateful
to know it.
I would be happy to hear about any reading experience. Being exact in mathematical 
language and maybe exercises.
Thanks a lot.

REPLY [3 votes]: Try Probability with Martingales, which I found to be very helpful for self-study. It's a short read but nevertheless concise and uses measure theory to introduce the basic concepts of probability theory.