Almost Everywhere

NAVIGATION

Home

Research

Bookshelf

Garden

FIND ME ON

GitHub

Home

Research

Bookshelf

Garden

Almost Everywhere

🌱

Definition

MeasureTheory

Let $(X,\mathcal{F},\mu)$ be a measure space. Let $P:X\to \{ T,F \}$ . We say property $P$ is “true” (i.e. $P=T$ ) $\mu$ -almost everywhere on $X$ (or almost surely) if $\mu(\{ x\in X:P(X)\not=T \})=0$

Linked from

A Summary of MATH 891

Radon-Nikodym Derivative

Equivalence between Density and Radon-Nikodym Derivative

Beppo Levi Theorem

Dominated Convergence Theorem

Lp Convergence

Integrals of Functions that are Zero a.e.

Scheffé's Theorem

Martingale Convergence Theorem