Abstract
We characterize those probability measures on the Bohr compactification of a metrizable, abelian group which admit a u. d. sequence in the original group. We show that the set of u. d. sequences on a nonmetrizable compact space can have the measure zero or one or it can be non-measurable. Finally we show that the existence of a u. d. sequence does not imply the existence of a well distributed sequence.
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