We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all BV functions and their total variation measures. In the setting of non-branching CD(K, N) spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.
On master test plans for the space of BV functions / Nobili, F., Pasqualetto, E., Schultz, T.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 16:4(2023), pp. 1061-1092. [10.1515/acv-2021-0078]
On master test plans for the space of BV functions
Nobili, F;
2023
Abstract
We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all BV functions and their total variation measures. In the setting of non-branching CD(K, N) spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.File in questo prodotto:
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