almost continuous function

Let m denote Lebesgue measureMathworldPlanetmath, A be a Lebesgue measurable subset of , and f:A (or f:A). Then f is almost continuousMathworldPlanetmath if, for every ε>0, there exists a closed subset F of such that FA, m(A-F)<ε, 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