University of Oulu

Falconer, K., Fraser, J., & Käenmäki, A. (2023). Minkowski dimension for measures. Proceedings of the American Mathematical Society, 151(2), 779–794.

Minkowski dimension for measures

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Author: Falconer, Kenneth J.1; Fraser, Jonathan M.1; Käenmäki, Antti2
Organizations: 1School of Mathematics and Statistics, University of St Andrews, KY16 9SS, United Kingdom
2Research Unit of Mathematical Sciences, P.O. Box 8000, FI-90014 University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: American Mathematical Society, 2023
Publish Date: 2023-03-17


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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Series: Proceedings of the American Mathematical Society
ISSN: 0002-9939
ISSN-E: 1088-6826
ISSN-L: 0002-9939
Volume: 151
Issue: 2
Pages: 779 - 794
DOI: 10.1090/proc/16174
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The first and second authors were financially supported by an EPSRC Standard Grant(EP/R015104/1) and the second author was supported by a Leverhulme Trust Research ProjectGrant (RPG-2019-034).
Copyright information: © Copyright 2022 American Mathematical Society.