The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon

Abstract

In this paper, we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E − the self-similar sets generating in a unit regular pentagon on the plane. Under some conditions, we show the natural covering is the best one, and the Hausdorff measures of those sets are equal to $|E|^s$, where $ s = dim_{H}E$.