| The Hausdorff Measure of a Class of Sierpinski Gaskets |
| Received:June 22, 2005 Revised:January 20, 2006 |
| Key Words:
self-similar set Sierpinski gasket Hausdorff measure.
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| Fund Project:the Scientific Research Fund of Chongqing Municipal Eucation Commission (Kj051206). |
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| Abstract: |
| Let $S_{\lambda}$ be a class of Sierpinski gaskets with compression ratio $\lambda~ (\lambda\leq\frac{1}{3})$, $s=-\log_{\lambda}^{3}$ be the Hausdorff dimension of $S_{\lambda}$, and $N$ be the set of all the basic triangles to produce $S_{\lambda}$. In the paper, by the method of net measure, the exact value of the Hausdorff measure of $S_{\lambda}$, $H^{s}(S_{\lambda})=1$, is obtained, the fact that the Hausdorff measure of $S_{\lambda}$ can be determined by net measure $H^{s}_{N}(S_{\lambda})$ is shown, and the best coverings of $S_{\lambda}$ that are nontrivial are obtained. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.04.023 |
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