Real Analysis Exchange

Absolutely Measurable Functions on Manifolds

Togo Nishiura

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Abstract

The paper is an investigation of the collection of absolutely measurable functions defined on compact, connected manifolds. Several analytical properties of these functions defined on the manifold $I$, the unit interval of $\mathbb R$, have been studied by C. Goffman, D. Waterman and the author in Homeomorphisms in analysis [Math. Surveys Monogr., Number 54, American Mathematical Society, Providence, 1997]. It will be shown that these properties also hold for all compact, connected manifolds. The method of proof differs from those used earlier for the interval $I$. The key element here is the use of the von Neumann-Ulam-Oxtoby Theorem for compact connected manifolds (proved here for the first time) which concerns measures induced by homeomorphisms.

Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 703-728.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285689146

Mathematical Reviews number (MathSciNet)
MR1704745

Zentralblatt MATH identifier
1039.28004

Subjects
Primary: 26B35: Special properties of functions of several variables, Hölder conditions, etc.

Keywords
absolutely measurable functions absolutely measurable sets universally measurable sets compact manifolds

Citation

Nishiura, Togo. Absolutely Measurable Functions on Manifolds. Real Anal. Exchange 24 (1999), no. 2, 703--728. https://projecteuclid.org/euclid.rae/1285689146


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