Pointwise Assouad dimension for measures
Classical Analysis and ODEs
2024-03-12 v2 Metric Geometry
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.
Cite
@article{arxiv.2203.15301,
title = {Pointwise Assouad dimension for measures},
author = {Roope Anttila},
journal= {arXiv preprint arXiv:2203.15301},
year = {2024}
}
Comments
28 pages; Incorporated suggestions made by the referee, Published in Proc. R. Soc. Edinb. A: Math