Probability Theory I

0.5 credit · Graduate

Probability spaces and probability measures, sigma-fields, random variables and distributions, expected values as Lebesgue integrals, change-of-variable formula, laws of large numbers, integral inequalities, convergence theorems, uniform integrability, product measures, Fubini's theorem, independence and related topics, Borel–Cantelli lemmas, maximal inequalities, modes of convergence, CLT, characteristic functions.