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 , the space of all Borel probability measures on . 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}
}