On asymptotic density and uniformly distributed sequences

Ryszard Frankiewicz; Grzegorz Plebanek

Studia Mathematica (1996)

  • Volume: 119, Issue: 1, page 17-26
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Frankiewicz, Ryszard, and Plebanek, Grzegorz. "On asymptotic density and uniformly distributed sequences." Studia Mathematica 119.1 (1996): 17-26. <http://eudml.org/doc/216282>.

@article{Frankiewicz1996,
abstract = {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.},
author = {Frankiewicz, Ryszard, Plebanek, Grzegorz},
journal = {Studia Mathematica},
keywords = {uniformly distributed sequences; asymptotic density; finitely additive measure; Martin's axiom; Radon measure},
language = {eng},
number = {1},
pages = {17-26},
title = {On asymptotic density and uniformly distributed sequences},
url = {http://eudml.org/doc/216282},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Frankiewicz, Ryszard
AU - Plebanek, Grzegorz
TI - On asymptotic density and uniformly distributed sequences
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 1
SP - 17
EP - 26
AB - 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.
LA - eng
KW - uniformly distributed sequences; asymptotic density; finitely additive measure; Martin's axiom; Radon measure
UR - http://eudml.org/doc/216282
ER -

References

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  1. [1] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges, Academic Press, London, 1983. Zbl0516.28001
  2. [2] W. W. Comfort, Topological groups, in: K. Kunen and J. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984, Chapter 24. 
  3. [3] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  4. [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. [5] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984. Zbl0551.03033
  6. [6] D. H. Fremlin, Postscript to Fremlin 84, preprint, 1991. 
  7. [7] L. Kuipers and H. Neiderreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. 
  8. [8] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces, Trans. Amer. Math. Soc. 246 (1978), 463-471. Zbl0409.10035
  9. [9] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces II, Monatsh. Math. 87 (1979), 247-260. Zbl0389.10035
  10. [10] S. Mercourakis, Some remarks on countably determined measures and uniform distribution of sequences, to appear. Zbl0901.28009

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