Real functions Monotone functions, bounded variation, absolute continuity Concept
Luzin N property
Summary
A function has the Luzin N property when it maps every set of Lebesgue measure zero to a set of Lebesgue measure zero. The property singles out the absolutely continuous functions among the continuous functions of bounded variation, by the Banach–Zarecki theorem. It also appears in the change of variables formula for Lebesgue integrals and in the study of Sobolev maps.
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| Tag | WMHMGJD261 |
|---|---|
| URI | m2://WMHMGJD261 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 26A46, 26A30 |
| Same as | |
| Changed | 2 November 2026 |
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