Intermediate value property for the Assouad dimension of measures
Classical Analysis and ODEs
2020-06-09 v2 Metric Geometry
Abstract
Hare, Mendivil, and Zuberman have recently shown that if is a compact subset of the reals and of non-zero Assouad dimension , then for all , supports measures with Assouad dimension . We generalise this result to arbitrary complete metric spaces.
Cite
@article{arxiv.2001.11306,
title = {Intermediate value property for the Assouad dimension of measures},
author = {Ville Suomala},
journal= {arXiv preprint arXiv:2001.11306},
year = {2020}
}
Comments
10 pages. Typos fixed. Proof for Lemma 2.3 included. To appear in Anal. Geom. Metr. Spaces