Back to Search
Start Over
A note on Hausdorff measures of self-similar sets in $\mathbb{R}^d$
- Source :
- Ann. Fenn. Math. 46(2), 957--963, 2021
- Publication Year :
- 2022
-
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].
- Subjects :
- Mathematics - Classical Analysis and ODEs
28A78, 28A80
Subjects
Details
- Database :
- arXiv
- Journal :
- Ann. Fenn. Math. 46(2), 957--963, 2021
- Publication Type :
- Report
- Accession number :
- edsarx.2201.01914
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.5186/aasfm.2021.4661