The Hausdorff measure of a Sierpinski-like fractal

Abstract

Let $S$ be a Sierpinski-like fractal with the compression ratio $\frac{1}{3}$, $N$ be the set of all the basic triangles to generate $S$. In this paper, by the mass distribution principle, the exact value of the Hausdorff measure of $S$, $H(S)=1$, is obtained, and the fact that the Hausdorff measure of $S$ can be determined by the net measure $H_N(S)$ is shown, and the best coverings of $S$ that are nontrivial are also obtained.