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)
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