Distribution of random Cantor sets on Tubes

Changhao Chen

We show that there exist $(d-1)$ - Ahlfors regular compact sets $E\subset {\mathbb{R}}^d,d\ge 2$ such that for any $t<d-1$, we have \[ \sup_T \frac{\mathcal{H}^{d-1}(E\cap T)}{…