On a relation between density measures and a certain flow

Ryoichi Kunisada, Nimish Shah

研究成果: Article

抄録

We study extensions of the asymptotic density to a finitely additive measure defined on all subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on natural numbers and investigate absolute continuity and singularity for those density measures. In particular, for any pair of such density measures we prove necessary and sufficient conditions that one is absolutely continuous with respect to the other and that they are singular. Also we prove similar results for weak absolute continuity and strong singularity. These results are formulated in terms of topological dynamics.

元の言語English
ページ(範囲)1941-1951
ページ数11
ジャーナルProceedings of the American Mathematical Society
147
発行部数5
DOI
出版物ステータスPublished - 2019 5 1

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Absolute Continuity
Natural number
Singularity
Finitely Additive Measure
Weak Continuity
Topological Dynamics
Asymptotic Density
Ultrafilter
Absolutely Continuous
Necessary Conditions
Subset
Sufficient Conditions
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

これを引用

On a relation between density measures and a certain flow. / Kunisada, Ryoichi; Shah, Nimish.

:: Proceedings of the American Mathematical Society, 巻 147, 番号 5, 01.05.2019, p. 1941-1951.

研究成果: Article

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