In a compact group G, a sequence (Fn) of finite sets is uniformly distributed if the averaging operators
are uniformly convergent to the mean for continuous complex-valued functions f. In any compact metric group, there are uniformly distributed sequences of finite sets which are determined by a metric for the group. In some compact groups, there are uniformly distributed sequences of finite sets which are determined by the algebraic structure. A necessary and sufficient condition for a sequence of finite sets to be uniformly distributed in a compact metric group is that for any metric d for G and each εG, there is a sequence of one-to-one maps pn: Fn→ Fn such that
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