Probability Theory

This is a course in mathematical probability that gives rigorous proofs to various limit theorems in probability (zero-one laws, laws of large numbers, central limit theorems) that, in particular, constitute a basis for most of the statistical techniques. Tentative topics are: Sigma-algebras of random events, probability measures; Random variables and their distributions, moments; Independent events and sigma-algebras, independent random variables; infinite products of probability spaces; Zero-One Laws and Laws of Large Numbers; Characteristic functions and their properties; Weak convergence of measures and central Limit Theorem; Radon-Nikodim theorem and conditional expectations. Prerequisites: 92.502 Measure and Integration or equivalent