On Uniformly Distributed Sequences of an Increasing Family of Finite Sets in Infinite-Dimensional Rectangles

Abstract

The concepts of uniformly distributed sequences of an increasing family of finite sets and Riemann integrability are considered in terms of the “Lebesgue measure” on infinite-dimensional rectangles in \(R^{\infty}\) and infinite-dimensional versions of famous results of Lebesgue and Weyl are proved.