English

A note on Hausdorff measures of self-similar sets in $\mathbb{R}^d$

Classical Analysis and ODEs 2022-01-07 v1

Abstract

We prove that for all s(0,d)s\in(0,d) and c(0,1)c\in (0,1) there exists a self-similar set ERdE\subset \mathbb{R}^d with Hausdorff dimension ss such that Hs(E)=cEs\mathcal{H}^s(E)=c|E|^s. This answers a question raised by Zhiying Wen[16].

Keywords

Cite

@article{arxiv.2201.01914,
  title  = {A note on Hausdorff measures of self-similar sets in $\mathbb{R}^d$},
  author = {Cai-Yun Ma and Yu-Feng Wu},
  journal= {arXiv preprint arXiv:2201.01914},
  year   = {2022}
}