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Zbl 1152.28005
Ambrosio, Luigi; Colesanti, Andrea; Villa, Elena
Outer Minkowski content for some classes of closed sets. (English)
[J] Math. Ann. 342, No. 4, 727-748 (2008). ISSN 0025-5831; ISSN 1432-1807/e

Summary: We find conditions ensuring the existence of the outer Minkowski content for $d$-dimensional closed sets in ${\Bbb{R}^d}$, 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.

MSC 2000:: *28A75 Geometric measure theory
49Q15 Geometric measure and integration theory, etc.

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