2 problems

Hausdorff-measure conjecture. If $\mathit{PH}_0(\operatorname{supp}\mu)$ is trivial and $0<\alpha<d$, then $$

Let $X_n$ be a random sample of $n$ points from a compact set $X\subseteq\mathbb{R}^m$, distributed according to a nonsingular probability measure $\mu$, where $m\geq 2$. Let…