Martingale Convergence Theorem: Proof and Stopping Time

This lecture covers the proof of the martingale convergence theorem, focusing on the key ingredient of maximal inequality for square-integrable martingales. The instructor explains the concept of stopping time and its application in the context of martingales, emphasizing the control over the behavior of the process. Various mathematical expressions and inequalities are derived to illustrate the convergence properties of martingales.