A question about Hausdorff measure

Question

Let $ \mathscr{H}^m $ be the m-dimensional Hausdorff measure in $ R^n $. Let $ m<k $ and $ A \subset R^n $. If $ \mathscr{H}^m(A) < \infty $ then $ \mathscr{H}^k (A) =0 $. How can i prove this fact?

Thank you