Minkowski dimension for measures

Falconer, Kenneth J.; Fraser, Jonathan M.; Käenmäki, Antti (2022-11-29)
 
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URL:
https://doi.org/10.1090/proc/16174

Falconer, Kenneth J.
Fraser, Jonathan M.
Käenmäki, Antti
American Mathematical Society
29.11.2022

Falconer, K., Fraser, J., & Käenmäki, A. (2023). Minkowski dimension for measures. Proceedings of the American Mathematical Society, 151(2), 779–794. https://doi.org/10.1090/proc/16174

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