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Lecture Notes on Measure-theoretic Probability Theory

Sebastien Roch, UW-Madison


These lecture notes are intended for a first semester of graduate-level measure-theoretic probability. Topics covered include: foundational material, independence, zero-one laws, laws of large numbers, weak convergence and the central limit theorem, conditional expectations and their properties, and martingales. The notes were used for a one-semester course at UW-Madison (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:

Lectures Notes

The notes are divided into one-week worth of material (two 75-minute lectures):

Last updated: December 2013.