Minkowski dimension for measures

Kenneth John Falconer; Jonathan Fraser; Antti Käenmäki

doi:10.1090/proc/16174

Minkowski dimension for measures

Kenneth John Falconer, Jonathan Fraser, Antti Käenmäki

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	779-794
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	2
Early online date	29 Nov 2022
DOIs	https://doi.org/10.1090/proc/16174
Publication status	Published - 1 Feb 2023

Keywords

Minkowski dimension
Assouad dimension
Doubling metric space

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10.1090/proc/16174Licence: Other

minkowski_dimensionV3
Copyright © 2022 American Mathematical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1090/proc/16174.
Accepted author manuscript, 346 KBLicence: CC BY-NC-ND

http://arxiv.org/abs/2001.07055

New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
The Leverhulme Trust
1/09/19 → 31/01/23
Project: Standard
Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
EPSRC
1/02/18 → 11/06/21
Project: Standard

Cite this

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author = "Falconer, {Kenneth John} and Jonathan Fraser and Antti K{\"a}enm{\"a}ki",

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KW - Doubling metric space

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Minkowski dimension for measures

Abstract

Keywords

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Projects

New perspectives in the dimension: New perspectives in the dimension theory of fractals

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this