Cardinal Functions of Purely Atomic Measures

Szymon Gła̧b, Jacek Marchwicki
2020 Results in Mathematics  
Let μ be a purely atomic finite measure. Without loss of generality we may assume that μ is defined on N, and the atoms with smaller indexes have larger masses, that is μ We study the problem for which sets R ⊂ {0, 1, 2, . . . , ω, c} there is a measure μ such that R = rng(fµ). We are also interested in the set-theoretic and topological properties of the set of μ-values which are obtained uniquely. Mathematics Subject Classification. Primary: 40A05, Secondary: 11K31.
doi:10.1007/s00025-020-01260-x fatcat:nmmrqiqljvgapcntinq7nue7ym