Lusin's theorem
Theorem in measure theory / From Wikipedia, the free encyclopedia
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This article is about the theorem of real analysis. For the separation theorem in descriptive set theory, see Lusin's separation theorem.
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. In the informal formulation of J. E. Littlewood, "every measurable function is nearly continuous".