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arXiv · 1305.7212

Lévy group and density measures

Martin Sleziak·Miloš Ziman
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Abstract

We will deal with finitely additive measures on integers extending the asymptotic density. We will study their relation to the Lévy group $\mathcal{G}$ of permutations of $\mathbb N$. Using a new characterization of the Lévy group $\mathcal G$ we will prove that a finitely additive measure extends density if and only if it is $\mathcal{G}$-invariant.

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Martin Sleziak, Miloš Ziman. 2013-05-30. Lévy group and density measures. https://doi.org/10.1016/j.jnt.2008.05.004

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