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

Giuseppina Barbieri; Giangiacomo Gerla

doi:10.12775/LLP.2022.031

Authors

Giuseppina Barbieri Department of Mathematics University of Salerno, Italy https://orcid.org/0000-0002-6460-1951
Giangiacomo Gerla Department of Mathematics University of Salerno, Italy

DOI:

https://doi.org/10.12775/LLP.2022.031

Keywords

measures, point-free structures, region-based theories of space

Abstract

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.

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