Calculus of Variations and Geometric Measure Theory
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F. Nobili - E. Pasqualetto - T. Schultz

On master test plans for the space of BV functions

created by pasqualetto on 13 Sep 2021



Inserted: 13 sep 2021

Year: 2021

ArXiv: 2109.04980 PDF


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.

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