Egorov’s theorem

Let $(X,\mathcal{S},\mu)$ be a measure space, and let $E$ be a subset of $X$ of finite measure. If $f_{n}$ is a sequence of measurable functions converging to $f$ almost everywhere, then for each $\delta>0$ there exists a set $E_{\delta}$ such that $\mu(E_{\delta})<\delta$ and $f_{n}\rightarrow f$ uniformly (http://planetmath.org/UniformConvergence) on $E-E_{\delta}$ .

Title	Egorov’s theorem
Canonical name	EgorovsTheorem
Date of creation	2013-03-22 13:13:46
Last modified on	2013-03-22 13:13:46
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 28A20
Synonym	Egoroff’s theorem