Definition (Measurable space)
Let be a set, and be a σ-algebra defined on . We say the pair is a measurable space.
A Summary of MATH 891
Measurability Criterion for Topological Codomain
Radon-Nikodym Theorem
Change of Variable Formula
Measure Space
Closure of Measurability
Composition of Measurable Functions
Criterion for Measurability
Measurable Function
Complete Measure Space
Measure
Pushforward Measure
Signed Measure
Fubini Theorem (For indicator functions)
Measurable Rectangle
Product σ-algebra
Witsenhausen's Intrinsic Model
Convergence in Expectation
Scheffé's Theorem
Probability Measure
Stochastic Kernel