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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Erdös 和Renyi关于Cantor级数统计性质研究的补充. |
| 关键词: Cantor展开 字符 Hausdorff维数 |
| DOI： |
| 分类号:O173.1 |
| 基金项目: |
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| A NOTE ON CANTOR EXPANSIONS OF REAL NUMBERS |
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HU Qian-li
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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. |
| Key words: Cantor expansion digit Hausdorff dimension |
