Assuming Martin's axiom we show that if X is a dyadic space of weight at most continuum then every Radon measure on X admits a uniformly distributed sequence. This answers a problem posed by Mercourakis [10]. Our proof is based on an auxiliary result concerning finitely additive measures on ω and asymptotic density.
Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
[1] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges, Academic Press, London, 1983.
[2] W. W. Comfort, Topological groups, in: K. Kunen and J. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, Chapter 24.
[3] R. Engelking, General Topology, PWN, Warszawa, 1977.
[4] R. Frankiewicz, Some remarks on embeddings of Boolean algebras, in: Measure Theory, Oberwolfach 1983, A. Dold and B. Eckmann (eds.), Lecture Notes in Math. 1089, Springer, 1984.
[5] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
[6] D. H. Fremlin, Postscript to Fremlin 84, preprint, 1991.
[7] L. Kuipers and H. Neiderreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
[8] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces, Trans. Amer. Math. Soc. 246 (1978), 463-471.
[9] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces II, Monatsh. Math. 87 (1979), 247-260.
[10] S. Mercourakis, Some remarks on countably determined measures and uniform distribution of sequences, to appear.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv119i1p17bwm
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