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arXiv · 1612.06286

A Federer-style characterization of sets of finite perimeter on metric spaces

Panu Lahti
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Abstract

In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that a set $E$ is of finite perimeter if and only if $\mathcal H(\partial^1 I_E)<\infty$, that is, if and only if the codimension one Hausdorff measure of the \emph{$1$-fine boundary} of the set's measure theoretic interior $I_E$ is finite.

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Panu Lahti. 2016-12-19. A Federer-style characterization of sets of finite perimeter on metric spaces. https://arxiv.org/abs/1612.06286

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