University of Oulu

Suomala, V. (2020). Intermediate Value Property for the Assouad Dimension of Measures. Analysis and Geometry in Metric Spaces, 8(1), 106–113.

Intermediate value property for the Assouad dimension of measures

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Author: Suomala, Ville1
Organizations: 1University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: De Gruyter, 2020
Publish Date: 2020-09-15


Hare, Mendivil, and Zuberman have recently shown that if \(X \subset \mathbb{R}\) is compact and of non-zero Assouad dimension \(\dim_{A} X\), then for all \(s > \dim_{A} X\), \(X\) supports measures with Assouad dimension \(s\). We generalize this result to arbitrary complete metric spaces.

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Series: Analysis and geometry in metric spaces
ISSN: 2299-3274
ISSN-E: 2299-3274
ISSN-L: 2299-3274
Volume: 8
Issue: 1
Pages: 106 - 113
DOI: 10.1515/agms-2020-0106
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The author was partially supported by the Academy of Finland CoE in Analysis and Dynamics research.
Copyright information: © 2020 Ville Suomala, published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License.