Finite Hausdorff Measure Implies Zero Higher Dimensional Measure

Theorem
Let $n \in \N_{>0}$.

Let $\R^n$ be the real Euclidean space.

Let $F \subseteq \R^n$.

Let $s \in \R_{\ge 0}$.

Then:
 * $\map {\HH^s} F < +\infty \implies \forall t \in \R_{>s} : \map {\HH^t} F = 0$