We provide general conditions, stable under finite unions, ensuring the existence of the outer Minkowski content ofBorel subsets ofRd . Such conditions turn out to be the same which guarantee the existence of the (d−1)-dimensionalMinkowski content of the boundary of the involved sets. Moreover, our results also apply to the study of the differentiability of the volume function of bounded sets, extending some known results in literature
On the outer Minkowski content of sets / E. Villa. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 188:4(2009), pp. 619-630.
On the outer Minkowski content of sets
E. VillaPrimo
2009
Abstract
We provide general conditions, stable under finite unions, ensuring the existence of the outer Minkowski content ofBorel subsets ofRd . Such conditions turn out to be the same which guarantee the existence of the (d−1)-dimensionalMinkowski content of the boundary of the involved sets. Moreover, our results also apply to the study of the differentiability of the volume function of bounded sets, extending some known results in literature
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