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Mathematics > Classical Analysis and ODEs

arXiv:2203.15301 (math)
[Submitted on 29 Mar 2022 (v1), last revised 11 Mar 2024 (this version, v2)]

Title:Pointwise Assouad dimension for measures

Authors:Roope Anttila
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Abstract:We introduce a pointwise variant of the Assouad dimension for measures on metric spaces, and study its properties in relation to the global Assouad dimension. We show that, in general, the value of the pointwise Assouad dimension differs from the global counterpart, but in many classical cases, it exhibits similar exact dimensionality properties as the classical local dimension, namely it equals the global Assouad dimension at almost every point. We also compute the Assouad dimension of invariant measures with place dependent probabilities supported on strongly separated self-conformal sets.
Comments: 28 pages; Incorporated suggestions made by the referee, Published in Proc. R. Soc. Edinb. A: Math
Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)
MSC classes: 28A80 (Primary), 28C15, 54E50 (Secondary)
Cite as: arXiv:2203.15301 [math.CA]
  (or arXiv:2203.15301v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2203.15301
Journal reference: Proc. R. Soc. Edinb. A: Math. (2023) 153(6):2053-2078
Related DOI: https://doi.org/10.1017/prm.2022.83

Submission history

From: Roope Anttila [view email]
[v1] Tue, 29 Mar 2022 07:44:02 UTC (26 KB)
[v2] Mon, 11 Mar 2024 10:22:24 UTC (23 KB)
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