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Elementary Numerosity and Measures by Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro is a scholarly article available to read on EtoBox.

What is Elementary Numerosity and Measures about?

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.

Author

Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro

Published

2012

Language

EN