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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 2, Pages 373-378
http://dx.doi.org/10.1155/S0161171290000552

On Fréchet theorem in the set of measure preserving functions over the unit interval

Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USA

Received 30 November 1988

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we study the Fréchet theorem in the set of measure preserving functions over the unit interval and show that any measure preserving function on [0,1] can be approximated by a sequence of measure preserving piecewise linear continuous functions almost everywhere. Some application is included.