Abstract
An elementary proof is given of the existence of a measure-preserving bijection of $\mathbb R^n$ that maps a preassigned Borel set with Lebesgue measure~$1$ onto the unit cube. The proof requires the use of only the Vitali Covering Theorem, translations and elementary properties of infinite sets.
Citation
Togo Nishiura. "Measure-Preserving Maps of ℝn." Real Anal. Exchange 24 (2) 837 - 842, 1998/1999.
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