Egorov’s theorem

Let (X,𝒮,μ) be a measure spaceMathworldPlanetmath, and let E be a subset of X of finite measure. If fn is a sequence of measurable functionsMathworldPlanetmath converging to f almost everywhere, then for each δ>0 there exists a set Eδ such that μ(Eδ)<δ and fnf uniformly ( on E-Eδ.

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