【测度概率论】MTP lecture 4-1

Discuss the measure- and Lebesgue integration theory that is relevant in probability theory.
Introduce some vital concepts in probability theory, such as conditional expectations, the Radon-Nikodym theorem, martingale convergence theorems, characteristic functions and why they are characteristic, the Brownian motion.
Provide rigorous proofs for two central convergence theorems in probability: the Strong Law of Large Numbers and the Central Limit Theorem.