Minkowski dimension for measures

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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.
Original languageEnglish
Pages (from-to)779-794
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number2
Early online date29 Nov 2022
Publication statusPublished - 1 Feb 2023


  • Minkowski dimension
  • Assouad dimension
  • Doubling metric space


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