On master test plans for the space of BV functions
We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $\rm BV$ functions and their total variation measures. In the setting of non-branching ${\sf CD}(K,N)$ spaces (with finite reference measure), we can additionally require these test p...
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| Sprache: | eng |
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| Zusammenfassung: | We prove that on an arbitrary metric measure space a countable collection of
test plans is sufficient to recover all $\rm BV$ functions and their total
variation measures. In the setting of non-branching ${\sf CD}(K,N)$ spaces
(with finite reference measure), we can additionally require these test plans
to be concentrated on geodesics. |
|---|---|
| DOI: | 10.48550/arxiv.2109.04980 |