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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) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe2023031732179 |
| Language: | English |
| Published: |
American Mathematical Society,
2023
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| Publish Date: | 2023-03-17 |
| Description: |
AbstractThe 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. see all
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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 |
| OADOI: | https://oadoi.org/10.1090/proc/16174 |
| Type of Publication: |
A1 Journal article – refereed |
| Field of Science: |
111 Mathematics |
| Subjects: | |
| 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. |