Konstantin Matveev
Introduction to Probability using Measure Theory
We will study Probability by taking a journey from Combinatorics to Measure Theory and back. The topics will include probability spaces and random variables from the measure theoretic framework, laws of large numbers and the Central limit theorem, zero-one laws, martingales, Markov chains and Brownian motion. Time permitting, we will touch on examples from modern research areas, such as statistical physics and random matrix theory.
Williams, Probability with martingales.
Real Analysis (640:501 or equivalent) and an undergraduate probability course at the level of Ross's text A first course in probability.