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Measures

Definition

Absolute Continuity

Definition

Almost Everywhere

Definition

Atomic Measure

Definition

Complete Measure Space

Definition

Counting measure

Definition

Dirac Measure

Definition

Elementary Set

Theorem

Fubini Theorem (For indicator functions)

Theorem

Fubini-Tonelli

Theorem

Hahn-Jordan Theorem

Definition

Lebesgue Measure

Definition

Measurable Rectangle

Definition

Measure

Definition

Monotone Class

Definition

Outer Measure

Theorem

Product Measure

Definition

Product σ-algebra

Theorem

Product σ-algebra is the smallest monotone class containing collection of elementary sets

Theorem

Properties of Measures

Definition

Pushforward Measure

Definition

Signed Measure

Theorem

Slices of P stay in their respective σ-algebras

Theorem

Slices of product measurable function are in measurable in resultant σ-algebras

Definition

Total Variation Measure