Abstract
The aim of this paper is to study the properties of the perimeter measure in the quite general setting of metric measure spaces. In particular, defining the essential boundary ∂* E of E as the set of points where neither the density of E nor the density of X∖E is 0, we show that the perimeter measure is concentrated on ∂* E and is representable by an Hausdorff-type measure.
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Ambrosio, L. Fine Properties of Sets of Finite Perimeter in Doubling Metric Measure Spaces. Set-Valued Analysis 10, 111–128 (2002). https://doi.org/10.1023/A:1016548402502
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DOI: https://doi.org/10.1023/A:1016548402502