Density measures and additive property

TL;DR

This paper investigates finitely additive measures extending natural density, focusing on a class constructed via ultrafilters and examining their additive properties.

Contribution

It introduces a class of density measures from ultrafilters and analyzes their additive properties, advancing understanding of density measure structures.

Findings

Ultrafilter-based density measures exhibit specific additivity properties.

The study characterizes when these measures are finitely additive.

Insights into the structure of density measures on natural numbers.

Abstract

We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural numbers and study a certain additivity property of such density measures.