On Diffeologies for Power Sets and Measures

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On Diffeologies for Power Sets and Measures

Ahmadi, Alireza; Magnot, Jean-Pierre

Set-valued and variational analysis, 12/2023, Volume: 31, Issue: 4

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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.

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