ABSTRACT
Readers are assumed to be familiar with the fundamentals of measure theory and probability theory in Loeve or Neveu, such as measure extension theorem,’ Radon-Nikodym theorem, dominated convergence theorem, Fatou’s lemma, Lp-space, Holder’s inequality, conditional mathematical expectation, Jensen’s inequality, conditional independence, product probability space and Fubini’s theorem. This chapter discusses Monotone class theorems, uniform integrability, essential suprema, and conditional expectation. It introduces the concept of analytic sets and their elementary properties.
