HAUSDORFF MEASURES OF A CLASS OF MORAN SETS.

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