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1998/1999 Absolutely Measurable Functions on Manifolds
Togo Nishiura
Real Anal. Exchange 24(2): 703-728 (1998/1999).


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.


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Togo Nishiura. "Absolutely Measurable Functions on Manifolds." Real Anal. Exchange 24 (2) 703 - 728, 1998/1999.


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

zbMATH: 1039.28004
MathSciNet: MR1704745

Primary: 26B35

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

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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