HAUSDORFF MEASURES of A CLASS of MORAN SETS

Let (n,c) be the class of Moran sets with integer n ≥ 2 and real c satisfying nc < 1. It is well known that the Hausdorff dimension of any set in this class is s = -logcn. We show that for any E (n,c), 2s 2 (n - 1)c 1 - cs ≤s(E) ≤ 1, where s(E) denotes s-dimensional Hausdorff measure of E. For any a with 2s 2 (n - 1)c 1 - cs ≤ a ≤ 1, there exists a self-similar set E (n,c) such that s(E) = a.