On diffeologies for power sets and measures
Differential Geometry
2023-03-22 v1 Optimization and Control
Abstract
We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link between the various diffeological structures that we propose, having in mind set-valued maps, relations, set-valued gradients, differentiable measures, and shape analysis. This work intends to establish rigorous properties on sample diffeologies that seem of interest to us.
Keywords
Cite
@article{arxiv.2303.11942,
title = {On diffeologies for power sets and measures},
author = {Alireza Ahmadi and Jean-Pierre Magnot},
journal= {arXiv preprint arXiv:2303.11942},
year = {2023}
}