Quantitative form of the Luzin $C$-property

• Date: 2010
• Main Authors: Krotov, V. G., Кротов, В. Г.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2874
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove the following statement, which is a quantitative form of the Luzin theorem on $C$-property: Let $(X, d, μ)$ be a bounded metric space with metric $d$ and regular Borel measure $μ$ that are related to one another by the doubling condition. Then, for any function $f$ measurable on $X$, there...