Lusin's Theorem states that for a measurable function on a measure space of finite measure, and for any chosen tolerance, there exists a continuous function that agrees with the original function everywhere except on a set of arbitrarily small measure. Named for Nikolai Lusin, it captures the informal principle that every measurable function is nearly continuous, and it is a standard structural result of real analysis and measure theory used in the study of approximation and integration.
Facts
Partially Attested
Proof YearYear is the publication year of Lusin's original paper in the reference list, not an explicit statement of the proof year. StatementAn almost-everywhere finite function is measurable if and only if it is a continuous function on nearly all its domain. 2 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Sources
1. Wikipedia: Lusin's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
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.
2. Lusin's theorem (Wikipedia)
Intro, sentence 1
an almost-everywhere finite function is measurable if and only if it is a continuous function on nearly all its domain
References, Sources, first entry (N. Lusin)
154 (1912)
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