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