Formulation of Convergence and Continuity in Variation of Sets in a Different Way from Sequences of Sets and Correspondence

The Continuity of Linear and Sublinear Correspondences Defined on Cones

In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.

The Continuity of $\mathbb{Q}_+$-Homogeneous Superadditive Correspondences

In this paper we investigate the continuity of $\mathbb{Q}_+$-homogeneous superadditive correspondences defined on the cones with finite basis in real topological vector spaces. It is also shown that every lower semicontinuous and $\mathbb{Q}_+$-homogeneous superadditive correspondence between two cones with finite basis admits a family of continuous linear selections.

通过测度值导子与BV-瓦瑟斯坦曲线建立度量空间上的连续性方程

Continuity equation on metric spaces via measure-valued derivations and BV-Wasserstein curves

本文引入度量空间上的连续性方程概念，基于测度值导子刻画配备1-瓦瑟斯坦距离的概率测度空间中的BV-曲线，其公式与Almi等人的相关工作一致，还扩展了此前的概率表示研究。