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.References
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Bibliographic Information
- Kenneth J. Falconer
- Affiliation: School of Mathematics and Statistics, University of St Andrews, KY16 9SS, United Kingdom
- MR Author ID: 65025
- Email: kjf@st-andrews.ac.uk
- Jonathan M. Fraser
- Affiliation: School of Mathematics and Statistics, University of St Andrews, KY16 9SS, United Kingdom
- MR Author ID: 946983
- ORCID: 0000-0002-8066-9120
- Email: jmf32@st-andrews.ac.uk
- Antti Käenmäki
- Affiliation: Research Unit of Mathematical Sciences, P.O. Box 8000, FI-90014 University of Oulu, Finland
- MR Author ID: 713182
- Email: antti.kaenmaki@oulu.fi
- Received by editor(s): February 1, 2022
- Received by editor(s) in revised form: June 8, 2022
- Published electronically: November 29, 2022
- Additional Notes: 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 Project Grant (RPG-2019-034).
- Communicated by: Katrin Gelfert
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 779-794
- MSC (2020): Primary 28A75, 28A80, 54E35; Secondary 28A78, 54F45
- DOI: https://doi.org/10.1090/proc/16174
- MathSciNet review: 4520027