| 关于实数Cantor级数展开的一个注记 |
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| 引用本文： | 胡千里.关于实数Cantor级数展开的一个注记[J].数学杂志,2014,34(2):303-305. |
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| 作者姓名： | 胡千里 |
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| 作者单位： | 清华大学数学系; |
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| 摘 要： | 本文主要研究实数的Cantor级数展开式.通过构造Moran集的方法,确定了由Cantor级数中不同字符个数的渐近值所定义的一类集合的Hausdorff维数.本文结果可视为Erd¨os和Renyi关于Cantor级数统计性质研究的补充.
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| 关 键 词： | Cantor展开 字符 Hausdorff维数 |
| 收稿时间： | 2013/9/20 0:00:00 |
| 修稿时间： | 2013/11/25 0:00:00 |
A NOTE ON CANTOR EXPANSIONS OF REAL NUMBERS |
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| HU Qian-li.A NOTE ON CANTOR EXPANSIONS OF REAL NUMBERS[J].Journal of Mathematics,2014,34(2):303-305. |
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| Authors: | HU Qian-li |
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| Institution: | Department of Mathematics, Tsinghua University, Beijing 100083, China |
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| Abstract: | This paper is mainly concerned with Cantor expansions of real numbers. By construction of Moran sets, Hausdorff dimensions of certain sets related to the number of distinct digits in the expansion are determined. It is a complement to the statistical properties studied by Erdös and Renyi. |
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| Keywords: | Cantor expansion digit Hausdorff dimension |
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