Minkowski dimension for measures

Falconer, Kenneth; Fraser, Jonathan; Käenmäki, Antti

doi:10.1090/proc/16174

Minkowski dimension for measures
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by Kenneth J. Falconer, Jonathan M. Fraser and Antti Käenmäki

Proc. Amer. Math. Soc. 151 (2023), 779-794

DOI: https://doi.org/10.1090/proc/16174

Published electronically: November 29, 2022

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Abstract:

The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we show that it can be used to characterise the Minkowski dimension of a compact metric space. We also study its relationship with other concepts in dimension theory.

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