# Lusin’s theorem

Let $A$ be a Lebesgue measurable subset of $\mathbb{R}$ and $f:A\to\mathbb{C}$ (or $f:A\to\mathbb{R}$). Then $f$ is Lebesgue measurable (http://planetmath.org/MeasurableFunctions) if and only if $f$ is almost continuous.

Title Lusin’s theorem LusinsTheorem 2013-03-22 16:13:48 2013-03-22 16:13:48 Wkbj79 (1863) Wkbj79 (1863) 6 Wkbj79 (1863) Theorem msc 28A20 MeasurableFunctions AlmostContinuousFunction