On the exact Hausdorff dimension of the set of Liouville numbers

Let L denote the set of Liouville numbers. For a dimension function h, we write H-h(L) for the h-dimensional Hausdorff measure of L. In this paper we locate the exact "cut-point" at which the Hausdorff measure of L drops from infinity to zero. Namely, if h is a dimension function that increases faster than any power function near 0, then H-h(L) = infinity, and if h is a dimension function that increases slower than some power function near 0, then H-h(L) = 0. This answers a question asked by R. D. Mauldin.