L\'evy group and density measures

Journal of Number Theory 128 (2008), 3005-3012 We will deal with finitely additive measures on integers extending the asymptotic density. We will study their relation to the L\'evy group $\mathcal{G}$ of permutations of $\mathbb N$. Using a new characterization of the L\'evy group $\mathca...

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Bibliographic Details
Main Authors Sleziak, Martin, Ziman, Miloš
Format Journal Article
LanguageEnglish
Published 30.05.2013
Subjects
Mathematics - Functional Analysis
Mathematics - Number Theory
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Summary:Journal of Number Theory 128 (2008), 3005-3012 We will deal with finitely additive measures on integers extending the asymptotic density. We will study their relation to the L\'evy group $\mathcal{G}$ of permutations of $\mathbb N$. Using a new characterization of the L\'evy group $\mathcal G$ we will prove that a finitely additive measure extends density if and only if it is $\mathcal{G}$-invariant.
DOI:10.48550/arxiv.1305.7212