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Miloš Ziman

Publications and source records attributed to Miloš Ziman.

2 recordsLinked to original sources
arXiv2013

Range of density measures

We investigate some properties of density measures -- finitely additive measures on the set of natural numbers $\N$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\big(\frac{A(n)}{n}\big)$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $\N$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao \cite{brbr} for general finitely additive measures. Also the values which can be attained by the measures defined in the first part of the paper are studied.

math.NT↗
arXiv2013

Lévy group and density measures

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.

math.NT↗