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These lecture notes are intended for a first-year graduate-level course on measure-theoretic probability. Topics covered include: foundations, independence, zero-one laws, laws of large numbers, weak convergence and the central limit theorem, conditional expectation, martingales, Markov chains and Brownian motion. The notes were used for two semester courses at UW-Madison (Spring 2018, Fall 2013) and two quarter courses at UCLA (Winter 2012, Winter 2011, Fall 2010, Winter 2010). The material is based largely on the following references:
The notes are divided into (roughly) one week worth of material (two 75-minute lectures):