On the Characterization of the Hausdorff Measure On a Quasi-Self-Similar Set

Abstract:

      In ［1］, the characterization of the Hausdorff measure on a self-similar set was given by siegfried GRFA. The concept of quasi-self-similar was introduced by John McLaughin in ［2］ and then some properties of the Hausdorff measure and dimension on quasi-self-similar sets were disscussed from［3］, K.J.Falconer. In this paper, we studied the characterization of the Hausdonff measure on a quasi-self-similar set and deduced that the Hausdorff measure is equavilent to some kind of measure which satisfied some conditions.