Convergence aspects for sets of measures with divergences and boundary conditions

TL;DR

This paper investigates convergence properties of vector-valued measures with divergences, boundary conditions, and applications, focusing on trace characterization, measure vanishing, and stability of optimization problems.

Contribution

It introduces a boundary trace characterization for measures, analyzes convergence of convex measure sets, and applies these results to optimization stability.

Findings

Boundary trace characterization for measures with divergences.

Convergence properties of convex measure sets with total variation bounds.

Applications to stability analysis in optimization problems.

Abstract

In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish subspaces of measures that directionally vanish in parts of the boundary, and present examples constructed with binary trees. Subsequently we study convex sets with total variation bounds and their convergence properties together with applications to the stability of optimization problems.