My intention is neither to learn basic probability concepts, nor to learn applications of the theory. My background is at the graduate level of having completed all engineering courses in probability/statistics — mostly oriented toward the applications without much emphasis on mathematical rigor.
Now I am very interested in learning the core logic and mathematical framework of probability theory, as a math branch. More specifically, I would like to learn answers to the following questions:
(1) What are the necessary axioms from which we can build probability theory?
(2) What are the core theorems and results in the mathematical theory of probability?
(3) What are the derived rules for reasoning/inference, based on the theorems/results in probability theory?
So I am seeking a book that covers the "heart" of mathematical probability theory — not needing much on applications, or discussion on extended topics.
I would like to appreciate your patience for reading my post and any informative responses.
Regards,
user36125
Best Answer
Williams, Probability with Martingales