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arXiv · 1804.11216

Federer's characterization of sets of finite perimeter in metric spaces

Panu Lahti
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Abstract

Federer's characterization of sets of finite perimeter states (in Euclidean spaces) that a set is of finite perimeter if and only if the measure-theoretic boundary of the set has finite Hausdorff measure of codimension one. In complete metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality, the "only if" direction was shown by Ambrosio (2002). By applying fine potential theory in the case $p=1$, we prove that the "if" direction holds as well.

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Panu Lahti. 2018-04-27. Federer's characterization of sets of finite perimeter in metric spaces. https://arxiv.org/abs/1804.11216

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