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outer minkowski content

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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A general formula for the anisotropic outer Minkowski content of a set
Part of
Luca Lussardi, Elena Villa
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 2 / April 2016

Published online by Cambridge University Press:

03 March 2016, pp. 393-413

Print publication:

April 2016
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We generalize to the anisotropic case some classical and recent results on the (n – 1)-Minkowski content of rectifiable sets in ℝn, and on the outer Minkowski content of subsets of ℝn. In particular, a general formula for the anisotropic outer Minkowski content is provided; it applies to a wide class of sets that are stable under finite unions.