On asymptotic density and uniformly distributed sequences

• Autorzy: Ryszard Frankiewicz , Grzegorz Plebanek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 11B05: Density, gaps, topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 1
• Strony: 17-26

Daty

wydano

1996

otrzymano

1995-04-27

poprawiono

1996-02-16

Twórcy

autor

Ryszard Frankiewicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland ,

autor

Grzegorz Plebanek

• 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.