Real Analysis Exchange

Measure-Preserving Maps of ℝn

Togo Nishiura

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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.

Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 837-842.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285689157

Mathematical Reviews number (MathSciNet)
MR1704756

Subjects
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
measure-preserving maps Borel measurable sets Vitali Covering Theorem

Citation

Nishiura, Togo. Measure-Preserving Maps of ℝ n. Real Anal. Exchange 24 (1999), no. 2, 837--842. https://projecteuclid.org/euclid.rae/1285689157


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