On Fréchet theorem in the set of measure preserving functions over the unit interval - So-Hsiang Chou; Truc T. Nguyen (International Journal of Mathematics and Mathematical Sciences)
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.