Probability Convergence

This lecture covers the concept of convergence in probability, discussing the conditions under which a sequence of random variables converges in probability. It explains the Kg-Fan metric and Borel-Cantelli lemmas, illustrating how to determine convergence and null sets. The lecture also delves into the uniqueness of convergence and the completeness of metric spaces. Additionally, it explores the relationship between convergence in probability and convergence almost surely, providing examples and exercises to reinforce the understanding of these concepts.