On a relation between density measures and a certain flow

Ryoichi Kunisada, Nimish Shah

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)1941-1951
Number of pages11
JournalProceedings of the American Mathematical Society
Volume147
Issue number5
DOIs
Publication statusPublished - 2019 May 1

Fingerprint

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

Keywords

  • Asymptotic density
  • Density measures
  • Finitely additive measures

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 147, No. 5, 01.05.2019, p. 1941-1951.

Research output: Contribution to journalArticle

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