Assume that \(\phi, \psi:[0, \infty) ightarrow[0, \infty)\) are admissible for the construction of Hausdorff measures and assume that \(\lim _{x ightarrow 0} \phi(x) / \psi(x)=0\). Show that \(\overline{\mathcal{H}}^{\psi}(A)<\infty\) implies \(\overline{\mathcal{H}}^{\phi}(A)=0\).