## Real Analysis Exchange

### Absolutely Measurable Functions on Manifolds

Togo Nishiura

#### 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