Fine properties of sets of finite perimeter in doubling metric measure spaces

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 partial derivative(*)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 partial derivative(*)E and is representable by an Hausdorff-type measure.