Publication at Faculty of Mathematics and Physics |
2022
Abstract
Let Gamma(E) be the family of all paths which meet a set E in the metric measure space X. The set function E bar right arrow AM (Gamma(E)) defines the AM-modulus measure in X where AM refers to the approximation modulus [22].
We compare AM (Gamma(E)) to the Hausdorff measure coH(1) (E) of codimension one in X and show that coH(1)(E) approximate to AM(Gamma(E)) for Suslin sets E in X. This leads to a new characterization of sets of finite perimeter in X in terms of the AM-modulus.
We also study the level sets of BV functions and show that for a.e. t. these sets have finite coH(1)-measure. Most of the results are new also in R-n.