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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
σ-algebra of subsets of
Measurable Function
Closure of Measurability
Composition of Measurable Functions
Criterion for Measurability
Complete Measure Space
Measure
Pushforward Measure
Signed Measure
Measurable Rectangle
Product σ-algebra
Fubini Theorem (For indicator functions)
Witsenhausen's Intrinsic Model
Convergence in Expectation
Scheffé's Theorem
Probability Measure
Disintegration