Elementary numerosity and measures
speaker: Emanuele Bottazzi (Università degli Studi di Trento)abstract: We introduce the notion of elementary numerosity, 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. It turns out that this notion is deeply related to the notion of measure: the main result is that every non-atomic finitely additive or sigma-additive measure is obtained from a suitable elementary numerosity by simply taking its ratio to a unit. The proof of this theorem relies on showing that, given a non-atomic finitely additive or sigma-additive measure over a set X, we can find an ultrafilter on X in a way that the corresponding elementary numerosity of a set can be defined as the equivalence class of a particular real X-sequence. We will show that, by this construction, the formal properties of finite cardinality are indeed transferred to this elementary numerosity. Applications of this result range from measure theory to non-archimedean probability.
timetable:
Fri 25 Jan, 17:10 - 17:50, Aula Dini
<< Go back