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arXiv · 1212.6201

Elementary numerosity and measures

Vieri Benci·Emanuele Bottazzi·Mauro Di Nasso
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Abstract

In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field, and satisfies the same formal properties of finite cardinality. We investigate the relationships between this notion and the notion of measure. The main result is that every non-atomic finitely additive measure is obtained from a suitable elementary numerosity by simply taking its ratio to a unit. In the last section we give applications to this result.

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Vieri Benci, Emanuele Bottazzi, Mauro Di Nasso. 2012-12-21. Elementary numerosity and measures. https://arxiv.org/abs/1212.6201

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