Convergence in Law: Theorem and Proof

This lecture covers the concept of convergence in law, discussing the conditions under which a sequence of random variables converges to a random variable. The instructor explains the implications of Kolmogorov's three series theorem and provides proofs based on lemmas related to convergence in probability. The lecture also delves into the Borel-Cantelli lemma and the representation theorem by Skorokhod. The importance of continuity in convergence is highlighted, along with the role of dominated convergence. Various examples and exercises are used to illustrate the theoretical concepts.