Hokkaido Mathematical Journal

WANG Ming-Hua,

The Hausdorff measure of a Sierpinski-like fractal.

Hokkaido Mathematical Journal, 36 (2007) pp.9-19

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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.

MSC(Primary)28A80
MSC(Secondary)28A78
Uncontrolled Keywordsself-similar set, Sierpinski-like fractal, Hausdorff measure, mass distribution principle