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A new proof of Lusin's theorem

Leon Cohen (1927)

Fundamenta Mathematicae

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The purpose of this paper is to give a new proof of the following Lusin's theorem: Théorème: If f(x) is a measurable function defined on the interval I: 0 ≤ x ≤ 1, then for every ϵ > 0 there is a set A ⊂ I such that f(x) is continuous on A and m(I-A) < ϵ.