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arXiv · 2201.01914

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

Cai-Yun Ma·Yu-Feng Wu
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Abstract

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

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Cai-Yun Ma, Yu-Feng Wu. 2022-01-06. A note on Hausdorff measures of self-similar sets in $\mathbb{R}^d$. https://doi.org/10.5186/aasfm.2021.4661

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