English

Quasi-Assouad dimensions for random measures supported on $[0,1]^d$

Metric Geometry 2019-09-26 v1 Probability

Abstract

We introduce a probability distribution on P([0,1]d)\mathcal{P}([0,1]^d), the space of all Borel probability measures on [0,1]d[0,1]^d. Under this distribution, almost all measures are shown to have infinite upper quasi-Assouad dimension and zero lower quasi-Assouad dimension (hence the upper and lower Assouad dimensions are almost surely infinite or zero). We also indicate how the results extend to other Assouad-like dimensions.

Keywords

Cite

@article{arxiv.1909.11132,
  title  = {Quasi-Assouad dimensions for random measures supported on $[0,1]^d$},
  author = {Wanchun Shen},
  journal= {arXiv preprint arXiv:1909.11132},
  year   = {2019}
}