Abstract
AbstractLet be the family of all paths which meet a set E in the metric measure space X. The set function defines the ‐modulus measure in X where refers to the approximation modulus [22]. We compare to the Hausdorff measure of codimension one in X and show that for Suslin sets E in X. This leads to a new characterization of sets of finite perimeter in X in terms of the ‐modulus. We also study the level sets of functions and show that for a.e. t these sets have finite ‐measure. Most of the results are new also in .
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