Egorov’s theorem

Let $(X,𝒮,\mu )$ 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 and $f_n\to f$ 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