Minimal Hausdorff Measure of the Scattered Cantor Sets
Received:August 22, 2007  Revised:May 21, 2008
Key Words: scattered Cantor set   minimal Hausdorff measure.
Fund Project:the National Natural Science Foundation of China (No.10771164); the Education Committee of Fujian Province (No.JA08155).
 Author Name Affiliation LI Jin Jun Department of Mathematics, Zhangzhou Normal University, Fujian 363000, China LU Shi Pan Teachers College, Jimei University, Fujian 361021, China
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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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