Lusin's theorem

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What Wikipedia says

In the mathematical field of mathematical analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an almost-everywhere finite function is measurable if and only if it is a continuous function on nearly all its domain.

Excerpt from the Wikipedia article “Lusin's theorem”, under the CC BY-SA 4.0 license. Read the article on Wikipedia