# On asymptotic density and uniformly distributed sequences

Ryszard Frankiewicz; Grzegorz Plebanek

Studia Mathematica (1996)

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

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topFrankiewicz, 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

top- [1] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges, Academic Press, London, 1983. Zbl0516.28001
- [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. Zbl0551.03033
- [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. Zbl0409.10035
- [9] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces II, Monatsh. Math. 87 (1979), 247-260. Zbl0389.10035
- [10] S. Mercourakis, Some remarks on countably determined measures and uniform distribution of sequences, to appear. Zbl0901.28009

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