Measure-preserving maps on \(\mathbb R^n\) (Q5932457)
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scientific article; zbMATH DE number 1602863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Measure-preserving maps on \(\mathbb R^n\) |
scientific article; zbMATH DE number 1602863 |
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Measure-preserving maps on \(\mathbb R^n\) (English)
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10 June 2001
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It is well known that for every Borel set \(B\subset \mathbb R^n\) with Lebesgue measure \(1\) there exists a measure-preserving bijection, mapping \(B\) onto the unit cube. This paper gives a real analytic proof, relying on Vitali's covering theorem.
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measure-preserving maps
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Borel sets
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covering theorem
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