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On the existence of uniformly distributed sequences in compact topological spaces II

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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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  1. Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    V. Losert

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  1. V. Losert
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Losert, V. On the existence of uniformly distributed sequences in compact topological spaces II. Monatshefte f#x00FC;r Mathematik 87, 247–260 (1979). https://doi.org/10.1007/BF01303079

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