English

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}
}
R2 v1 2026-06-28T09:26:36.069Z