A note on the Luzin-Menchoff theorem (Q1664057)
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scientific article; zbMATH DE number 6924885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the Luzin-Menchoff theorem |
scientific article; zbMATH DE number 6924885 |
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A note on the Luzin-Menchoff theorem (English)
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24 August 2018
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A refinement of the Luzin-Menchoff theorem is given. It states that for every closed subset \(K\) of a measurable \(E\subset\mathbb R^n\) there is a closed set \(F\) such that \(K\subset F\subset E\), the upper densities of \(F\) and \(E\) at points of \(K\) coincide, the lower densities of \(F\) and \(E\) at points of \(K\) coincide, and the density of \(E\) at points of \(F\setminus K\) is one.
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Luzin-Menchoff property
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density
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measurable set
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