On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Abstract

Abstract Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type μC↦∫01∫01FdμC, {\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,} where µC is a copula measure and F is a Riemann integrable function on [0, 1]2 of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.