Abstract.
In our earlier paper (Arch. Math. 91 (2008), 76–85), we proved that if F is a sequence of finite nonempty subsets of \({\mathbb{N}}\) such that a certain quantity t(F) is finite, then the associated submeasure d F on \({\mathbb{N}}\) is nonatomic. In the present note, we give two curious characterizations of the set of such sequences F.
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Received: 10 December 2008
The second author is partially supported by the Foundation for Polish Science.
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Drewnowski, L., łuczak, T. On nonatomic submeasures on \({\mathbb{N}}\). III. Arch. Math. 92, 377–382 (2009). https://doi.org/10.1007/s00013-009-3140-3
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DOI: https://doi.org/10.1007/s00013-009-3140-3