Geodesic
A note on Hausdorff measures of self-similar sets in R^d
Cai-Yun Ma1 ; Yu-Feng Wu2
1 The Chinese University of Hong Kong, Department of Mathematics
2 South China University of Technology, Department of Mathematics, and The Chinese University of Hong Kong, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 957-963 Cet article a éte moissonné depuis la source Journal.fi

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

Cai-Yun Ma 1 ; Yu-Feng Wu 2

1 The Chinese University of Hong Kong, Department of Mathematics
2 South China University of Technology, Department of Mathematics, and The Chinese University of Hong Kong, Department of Mathematics 
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Cai-Yun Ma; Yu-Feng Wu. A note on Hausdorff measures of self-similar sets in R^d. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 957-963. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a20/