Measure Theory and Probability Theory Study Guide

Study Guide compiled by Cory Lanker and Luke Fostvedt, Iowa State University
Content includes: Sigma Algebras, Measurable Sets, Lebesgue Measures, Lebesgue Integration, General Lebesgue Integrals, Product Measures, Radon-Nikodym Theorem, Fubini and Tonelli’s theorems, Lebesgue Fundamental Theorem of Calculus, Inequalities, Independence, Borel-Cantelli Lemmas, Law of Large Numbers, Convergence in Probability, Convergence is Distribution, Kolmogorov Theorems, Continuous Mapping Theorem, Tightness, and Method of Moments.

Source: class notes by Dan Nordman, Fall 2009, STAT642, and “Real Analysis” by H. Royden and “Measure Theory” by P.R. Halmos. All references in this document are to Professor Dan Nordman’s class notes.
Content: This study guide is a good supplement to the Athreya Lahiri Text.

Study Guide: Measure Theory and Probability Theory Study Guide