Effectivizing Lusin's Theorem

Abstract

Lusin’s Theorem states that, for every Borel-measurable function f on ℝ and every ε > 0, there exists a continuous function g on ℝ which is equal to f except on a set of measure < ε. We give a proof of this result using computability theory, relating it to the near-uniformity of the Turing jump operator, and use this proof to derive several uniform computable versions.