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Elementary numerosity and measures. (English) Zbl 1300.26018

Summary: In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set \(\Omega\) which takes values in a suitable non-Archimedean field and satisfies the same formal properties as finite cardinality. By improving a classic result by C. W. Henson in nonstandard analysis, we prove a general compatibility result between such elementary numerosities and measures.

MSC:

26E30 Non-Archimedean analysis
28E15 Other connections with logic and set theory
26E35 Nonstandard analysis
60A05 Axioms; other general questions in probability
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