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2020 Federer's characterization of sets of finite perimeter in metric spaces
Panu Lahti
Anal. PDE 13(5): 1501-1519 (2020). DOI: 10.2140/apde.2020.13.1501

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 1. In complete metric spaces that are equipped with a doubling measure and support a Poincaré 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. "Federer's characterization of sets of finite perimeter in metric spaces." Anal. PDE 13 (5) 1501 - 1519, 2020. https://doi.org/10.2140/apde.2020.13.1501

Information

Received: 27 April 2018; Revised: 3 January 2019; Accepted: 12 May 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07271836
MathSciNet: MR4149068
Digital Object Identifier: 10.2140/apde.2020.13.1501

Subjects:
Primary: 26B30 , 30L99 , 31E05

Keywords: codimension-1 Hausdorff measure , Federer's characterization , Fine topology , measure-theoretic boundary , metric measure space , set of finite perimeter

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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