On master test plans for the space of BV functions

Abstract

We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $\mathrm{BV}$ functions and their total variation measures. In the setting of non-branching $\mathsf{CD}(K,N)$ spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.

35 pages