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

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Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type μC0101FdμC,{\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.