Elementary numerosity and measures

Abstract

In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set Ω which takes values in a\rsuitable 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.