Pointwise Assouad dimension for measures
Anttila, Roope (2022-12-21)
Cambridge University Press
21.12.2022
Anttila, R. (2023). Pointwise Assouad dimension for measures. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153(6), 2053-2078. doi:10.1017/prm.2022.83
https://rightsstatements.org/vocab/InC/1.0/
This article has been published in a revised form in Proceedings of the Royal Society of Edinburgh section A: mathematics [https://doi.org/10.1017/prm.2022.83]. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
https://rightsstatements.org/vocab/InC/1.0/
This article has been published in a revised form in Proceedings of the Royal Society of Edinburgh section A: mathematics [https://doi.org/10.1017/prm.2022.83]. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202312043495
https://urn.fi/URN:NBN:fi:oulu-202312043495
Tiivistelmä
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 may differ from the global counterpart, but in many classical cases, the pointwise Assouad dimension exhibits similar exact dimensionality properties as the classical local dimension, namely it equals the global Assouad dimension almost everywhere. We also prove an explicit formula for the Assouad dimension of certain invariant measures with place-dependent probabilities supported on self-conformal sets.
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 may differ from the global counterpart, but in many classical cases, the pointwise Assouad dimension exhibits similar exact dimensionality properties as the classical local dimension, namely it equals the global Assouad dimension almost everywhere. We also prove an explicit formula for the Assouad dimension of certain invariant measures with place-dependent probabilities supported on self-conformal sets.
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