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Integrable

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Definition

MeasureTheory

Let $f:X\to \mathbb{R}$ measurable. $f$ is called integrable if $\int\limits _{X}|f| \, d\mu<\infty$

$f\text{ measurable}\implies|f|\text{ measurable}$ by Composition of Measurable Functions.

Linked from

A Summary of MATH 891

Set of all Integrable Functions

Integrals of Functions that are Zero a.e.

Four Hypotheses

Stationary Radner Krainak Theorem

Scheffé's Theorem

Conditional Expectation

Expectation

Markov's Inequality

σ(X)

Summary of MATH 895

Quadratic Variation is CAII

Martingale

Submartingale

Supermartingale

Doob's Optional Sampling Theorem

Martingale Convergence Theorem