almost continuous function

Let $m$ denote Lebesgue measure, $A$ be a Lebesgue measurable subset of $\mathbb{R}$ , and $f:A\to\mathbb{C}$ (or $f:A\to\mathbb{R}$ ). Then $f$ is almost continuous if, for every $\varepsilon>0$ , there exists a closed subset $F$ of $\mathbb{R}$ such that $F\subseteq A$ , $m(A-F)<\varepsilon$ , and $f|_{F}$ is continuous.

Title	almost continuous function
Canonical name	AlmostContinuousFunction
Date of creation	2013-03-22 16:13:45
Last modified on	2013-03-22 16:13:45
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	4
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 28A20
Synonym	almost continuous
Related topic	LusinsTheorem2