## Real Analysis Exchange

### Measure-Preserving Maps of ℝn

Togo Nishiura

#### 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

https://projecteuclid.org/euclid.rae/1285689157

Mathematical Reviews number (MathSciNet)
MR1704756

#### Citation

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