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1998/1999 Measure-Preserving Maps of ℝn
Togo Nishiura
Real Anal. Exchange 24(2): 837-842 (1998/1999).


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.


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Togo Nishiura. "Measure-Preserving Maps of ℝn." Real Anal. Exchange 24 (2) 837 - 842, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

MathSciNet: MR1704756

Primary: 28A05

Keywords: Borel measurable sets , measure-preserving maps , Vitali Covering Theorem

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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