A note on Hausdorff measures of self-similar sets in R^d

Cai-Yun Ma; Yu-Feng Wu

Geodesic

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A note on Hausdorff measures of self-similar sets in R^d

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

Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 957-963.

Voir la notice de l'article provenant de la source Journal.fi

Résumé

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

Affiliations des auteurs :

Cai-Yun Ma ¹ ; Yu-Feng Wu ²

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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/