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arXiv · 1207.3279

Invariance of the normalized Minkowski content with respect to the ambient space

Maja Resman
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Abstract

It is easy to show that the lower and the upper box dimensions of a bounded set in Euclidean space are invariant with respect to the ambient space. In this article we show that the Minkowski content of a Minkowski measurable set is also invariant with respect to the ambient space when normalized by an appropriate constant. In other words, the value of the normalized Minkowski content of a bounded, Minkowski measurable set is intrinsic to the set.

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Maja Resman. 2012-07-12. Invariance of the normalized Minkowski content with respect to the ambient space. https://doi.org/10.1016/j.chaos.2013.10.001

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