On the exact Hausdorff dimension of the set of Liouville numbers

Let denote the set of Liouville numbers. For a dimension function h, we write () for the h-dimensional Hausdorff measure of . In this paper we locate the exact cut-point at which the Hausdorff measure of drops from infinity to zero. Namely, if h is a dimension function that increases faster than any power function near 0, then ()=, and if h is a dimension function that increases slower than some power function near 0, then ()=0. This answers a question asked by R. D. Mauldin.Mathematics Subject Classification (2000): 28A80