Cardinal functions of purely atomic measures

2019/11/04 by Głab, Szymon, Marchwicki, Jacek · 2 citations
#11K31 #40A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.01206

Abstract

Let μ be a purely atomic measure. By f_μ:[0,∞)→\0,1,2,…,ω,\mathfrakc\ we denote its cardinal function f_μ(t)=\vert\A⊂\mathbb N:μ(A)=t\\vert. We study the problem for which sets R⊂\0,1,2,…,ω,\mathfrakc\ there is a measure μ such that R is the range of f_μ. We are also interested in the set-theoretic and topological properties of the set of μ-values which are obtained uniquely.

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• Achievement sets -- current results and open problems
• Bounded ranges of cardinal functions

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