Measures in Euclidean Point-Free Geometry (an exploratory paper)

We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.

Automated summary

This article addresses the question of a suitable measure theory in Euclidean point-free geometry and outlines some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the concept of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.