| Minimal Hausdorff Measure of the Scattered Cantor Sets |
| Received:August 22, 2007 Revised:May 21, 2008 |
| Key Words:
scattered Cantor set minimal Hausdorff measure.
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| Fund Project:the National Natural Science Foundation of China (No.10771164); the Education Committee of Fujian Province (No.JA08155). |
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| Abstract: |
| In this paper, we construct a scattered Cantor set having the value $\frac{1}{2}$ of $\frac{\log 2}{\log 3}$-dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value $\frac{1}{2}$ is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.06.023 |
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