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. https://doi.org/10.1515/agms-2020-0106

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)
Persistent link: http://urn.fi/urn:nbn:fi-fe2020091569496
Language: English
Published: De Gruyter, 2020
Publish Date: 2020-09-15
Description:

Abstract

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
OADOI: https://oadoi.org/10.1515/agms-2020-0106
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
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.
  https://creativecommons.org/licenses/by/4.0/