Calculating Hausdorff dimension in higher dimensional spaces

M. A. Sánchez-Granero, M. Fernández-Martínez

In this paper, we prove the identity ${\dim }_{\text{H}}(F)=d\cdot {\dim }_{\text{H}}({\alpha }^{-1}(F))$, where ${\dim }_{\text{H}}$ denotes Hausdorff dimension, $F\subseteq {\mathbb{R}}^d$, and…