  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.
