English

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 ERE\subseteq \mathbb{R} is positive, then given any D>dimAED>\dim_{A}E there is a measure with support EE and upper Assouad (or regularity) dimension DD. Similarly, given any 0d<dimLE,0\leq d<\dim_{L}E, there is a measure on EE with lower Assouad dimension dd.

Keywords

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}
}
R2 v1 2026-06-23T10:46:12.598Z