Measures with specified support and arbitrary Assouad dimensions
Classical Analysis and ODEs
2019-08-14 v1
Abstract
We show that if the upper Assouad dimension of the compact set is positive, then given any there is a measure with support and upper Assouad (or regularity) dimension . Similarly, given any there is a measure on with lower Assouad dimension .
Cite
@article{arxiv.1908.04592,
title = {Measures with specified support and arbitrary Assouad dimensions},
author = {Kathryn E. Hare and Franklin Mendivil and Leandro Zuberman},
journal= {arXiv preprint arXiv:1908.04592},
year = {2019}
}