The Hausdorff measure of a Sierpinski-like fractal (Q2467077)

Let \(S\) be a Sierpinski-like fractal with the compression ratio \(1/3\). \(N\) 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.