Math 170e - Study guides, Class notes & Summaries

This is a course note for the course MATH 170A Probability Theory I in UCLA. It provides an introduction to graduate-level advanced probability theory. It starts from the basic elements of probability: sets, probability axioms, conditional probability, total probability theorem and Bayes rule. Then it delves into measure-theoretic introduction of integration, Fubini's theorem, Borel-Cantelli theorem, Kolmogorov zero-one law, characteristic function, different convergence modes of random varia...