### 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.

#### Keywords

computability; computable analysis; Lusin's Theorem

#### Full Text:

3. [PDF]DOI: https://doi.org/10.4115/jla.2022.14.3

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Journal of Logic and Analysis ISSN: 1759-9008