# 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 EgorovsTheorem 2013-03-22 13:13:46 2013-03-22 13:13:46 Koro (127) Koro (127) 6 Koro (127) Theorem msc 28A20 Egoroff’s theorem