Elementary numerosity and measures
Functional Analysis
2012-12-27 v1
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.
Keywords
Cite
@article{arxiv.1212.6201,
title = {Elementary numerosity and measures},
author = {Vieri Benci and Emanuele Bottazzi and Mauro Di Nasso},
journal= {arXiv preprint arXiv:1212.6201},
year = {2012}
}
Comments
16 pages