On Diffeologies for Power Sets and Measures

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED Set-Valued and Variational Analysis Pub Date : 2023-11-21 DOI:10.1007/s11228-023-00703-1

Alireza Ahmadi, Jean-Pierre Magnot

引用次数: 1

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.

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论功率集与测度的微分

考虑幂集和Borel代数上的微分几何集。我们选择的框架是基于微分学的，我们在我们提出的各种微分结构之间建立了联系，在脑海中有集值映射、关系、集值梯度、可微测度和形状分析。这项工作旨在建立我们感兴趣的样品微分学的严格性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.

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