Convergence in Law: Weak Convergence and Skorokhod's Representation Theorem

This lecture covers the concept of convergence in law, focusing on weak convergence and Skorokhod's representation theorem. It explains how sequences of random variables converge to a measure, the conditions for weak convergence, and the representation of convergence in distribution. The theorem is presented, showing the convergence of sequences of random variables to another random variable in law. The proof involves demonstrating the convergence of continuous and bounded functions. The lecture also discusses the implications of the theorem and its applications in probability theory.