On a relation between density measures and a certain flow

Ryoichi Kunisada, Nimish Shah

研究成果: Article査読

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.

本文言語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
5
DOI
出版ステータスPublished - 2019 5 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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