Hausdorff Measures of a Class of Moran Sets

Abstract

Let [Formula: see text] be the class of Moran sets with integer [Formula: see text] and real [Formula: see text] satisfying [Formula: see text]. It is well known that the Hausdorff dimension of any set in this class is [Formula: see text]. We show that for any [Formula: see text], [Formula: see text] where [Formula: see text] denotes [Formula: see text]-dimensional Hausdorff measure of [Formula: see text]. For any [Formula: see text] with [Formula: see text] there exists a self-similar set [Formula: see text] such that [Formula: see text].