International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 373-378
doi:10.1155/S0161171290000552
On Fréchet theorem in the set of measure preserving functions over the unit interval
So-Hsiang Chou
and Truc T. Nguyen
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USA
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.