Probability Theory: Conditional Expectation

This lecture covers conditional expectation, the best G-measurable approximation of a random variable, and the convergence of random variables. It delves into the concept of regular conditional distribution and presents various propositions and proofs related to conditional expectation. The lecture also discusses Paley-Zygmund inequality and the strong law of large numbers, emphasizing the convergence of random variables. Furthermore, it explores the concept of almost sure convergence along geometric subsequences and provides detailed explanations and proofs for each concept.