  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.
