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

Durante, Fabrizio; Fernández-Sánchez, Juan; Ignazzi, Claudio; Trutschnig, Wolfgang

doi:10.2478/udt-2020-0013

Abstract

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type $μ_{C} \mapsto \int_{0}^{1} {\int_{0}^{1} F d}_{μ}_{C},$ {\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,} where µ_C 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.

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

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