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

Authors

  • Cai-Yun Ma The Chinese University of Hong Kong, Department of Mathematics
  • Yu-Feng Wu South China University of Technology, Department of Mathematics, and The Chinese University of Hong Kong, Department of Mathematics

Keywords:

Self-similar sets, Hausdorff measure

Abstract

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].
Issue
Vol. 46 No. 2 (2021)
Section
Articles

Published

2021-08-19

How to Cite

Ma, C.-Y., & Wu, Y.-F. (2021). A note on Hausdorff measures of self-similar sets in R^d. Annales Fennici Mathematici, 46(2), 957–963. Retrieved from https://afm.journal.fi/article/view/110908

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