We find conditions ensuring the existence of the outer Minkowski content for d-dimensional closed sets in R^d , in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class
Outer Minkowski content for some classes of closed sets / L. Ambrosio, A. Colesanti, E. Villa. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 342:4(2008), pp. 727-748.
Outer Minkowski content for some classes of closed sets
E. VillaUltimo
2008
Abstract
We find conditions ensuring the existence of the outer Minkowski content for d-dimensional closed sets in R^d , in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class
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