| 扩散 Cantor 集的最小Hausdorff 测度 |
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| 引用本文： | 李进军,陆式盘. 扩散 Cantor 集的最小Hausdorff 测度[J]. 数学研究及应用, 2009, 29(6): 1114-1116. DOI: 10.3770/j.issn:1000-341X.2009.06.022 |
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| 作者姓名： | 李进军 陆式盘 |
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| 作者单位： | 漳州师范学院数学与信息科学系, 福建 漳州 363000;集美大学教育学院, 福建 厦门 361021 |
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| 基金项目： | 国家自然科学基金(No.10771164);福建省教育厅科技项目(No.JA08155). |
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| 摘 要： | In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek.
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| 关 键 词： | Hausdorff测度 Cantor集 康托尔集 分散 定理 |
| 收稿时间： | 2007-08-22 |
| 修稿时间： | 2008-05-21 |
Minimal Hausdorff Measure of the Scattered Cantor Sets |
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| LI Jin Jun and LU Shi Pan. Minimal Hausdorff Measure of the Scattered Cantor Sets[J]. Journal of Mathematical Research with Applications, 2009, 29(6): 1114-1116. DOI: 10.3770/j.issn:1000-341X.2009.06.022 |
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| Authors: | LI Jin Jun and LU Shi Pan |
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| Affiliation: | Department of Mathematics, Zhangzhou Normal University, Fujian 363000, China;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. |
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| Keywords: | scattered Cantor set minimal Hausdorff measure. |
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