Range of density measures

Martin Sleziak; Miloš Ziman

Acta Mathematica Universitatis Ostraviensis (2009)

  • Volume: 17, Issue: 1, page 33-50
  • ISSN: 1804-1388

Abstract

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We investigate some properties of density measures – finitely additive measures on the set of natural numbers ℕ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence A ( n ) n as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of ℕ . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao, M., Theory of Charges – A Study of Finitely Additive Measures, Academic Press, London–New York, 1983.] for general finitely additive measures. Also the values which can be attained by the measures defined in the first part of the paper are studied.

How to cite

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Sleziak, Martin, and Ziman, Miloš. "Range of density measures." Acta Mathematica Universitatis Ostraviensis 17.1 (2009): 33-50. <http://eudml.org/doc/35196>.

@article{Sleziak2009,
abstract = {We investigate some properties of density measures – finitely additive measures on the set of natural numbers $\text\{$\mathbb \{N\}$\}$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\bigl (\frac\{A(n)\}\{n\}\bigr )$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $\text\{$\mathbb \{N\}$\}$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao, M., Theory of Charges – A Study of Finitely Additive Measures, Academic Press, London–New York, 1983.] for general finitely additive measures. Also the values which can be attained by the measures defined in the first part of the paper are studied.},
author = {Sleziak, Martin, Ziman, Miloš},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {asymptotic density; density measure; finitely additive measure; asymptotic density; density measure; finitely additive measure},
language = {eng},
number = {1},
pages = {33-50},
publisher = {University of Ostrava},
title = {Range of density measures},
url = {http://eudml.org/doc/35196},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Sleziak, Martin
AU - Ziman, Miloš
TI - Range of density measures
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2009
PB - University of Ostrava
VL - 17
IS - 1
SP - 33
EP - 50
AB - We investigate some properties of density measures – finitely additive measures on the set of natural numbers $\text{$\mathbb {N}$}$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\bigl (\frac{A(n)}{n}\bigr )$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $\text{$\mathbb {N}$}$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao, M., Theory of Charges – A Study of Finitely Additive Measures, Academic Press, London–New York, 1983.] for general finitely additive measures. Also the values which can be attained by the measures defined in the first part of the paper are studied.
LA - eng
KW - asymptotic density; density measure; finitely additive measure; asymptotic density; density measure; finitely additive measure
UR - http://eudml.org/doc/35196
ER -

References

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