Some Properties of Uniformly Distributed Sequences

Abstract

We show that if a transformation T on the unit interval is surjective, piecewise continuously differentiable, and uniform distribution preserving, then every u.d. sequence mod 1 is the image of some other u.d. sequence mod 1 induced by T. As a consequence, we obtain that every ud. sequence mod 1 can be decomposed into finitely many sequences with given asymptotic densities and asymptotic distribution functions. © 1993 Academic Press. All rights reserved.