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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| creator | Nobili, Francesco Pasqualetto, Enrico Schultz, Timo |
| description | 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_str_mv | 10.48550/arxiv.2109.04980 |
| format | Article |
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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
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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
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to be concentrated on geodesics.</abstract><doi>10.48550/arxiv.2109.04980</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Differential Geometry Mathematics - Functional Analysis Mathematics - Metric Geometry |
| title | On master test plans for the space of BV functions |
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