Hausdorff measure of cartesian product of Cantor sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911203611115520 |
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| author | Guo, Siyuan Jones, Taylor |
| author_facet | Guo, Siyuan Jones, Taylor |
| contents | Hausdorff measure and Hausdorff dimension are useful tools to describe fractals. This paper investigates the bounds on the $d\log_32$-dimensional Hausdorff measure of the $d$-fold Cartesian product of the $1/3$ Cantor set, $\mathcal C^d$. By applying known theorems on the Hausdorff measure of fractals satisfying the strong open set condition and generalizing what has been done on $\mathcal C^2$, we compute stricter upper and lower bounds for the Hausdorff measure of $\mathcal C^d$ for several small integers $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hausdorff measure of cartesian product of Cantor sets Guo, Siyuan Jones, Taylor Classical Analysis and ODEs Dynamical Systems 28A80 Hausdorff measure and Hausdorff dimension are useful tools to describe fractals. This paper investigates the bounds on the $d\log_32$-dimensional Hausdorff measure of the $d$-fold Cartesian product of the $1/3$ Cantor set, $\mathcal C^d$. By applying known theorems on the Hausdorff measure of fractals satisfying the strong open set condition and generalizing what has been done on $\mathcal C^2$, we compute stricter upper and lower bounds for the Hausdorff measure of $\mathcal C^d$ for several small integers $d$. |
| title | Hausdorff measure of cartesian product of Cantor sets |
| topic | Classical Analysis and ODEs Dynamical Systems 28A80 |
| url | https://arxiv.org/abs/2510.09701 |