| 关于自相似集的Hausdorff测度 |
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| 引用本文： | 文胜友,许绍元.关于自相似集的Hausdorff测度[J].数学学报,2001,44(1):117-124. |
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| 作者姓名： | 文胜友 许绍元 |
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| 作者单位： | 1. 韩山师范学院数学系;武汉大学数学系
2. 淮北煤炭师范学院数学系 |
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| 基金项目： | 淮北煤炭师范学院及韩山师范学院科研基金资助项目 |
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| 摘 要： | 得到了 Ｈａｕｓｄｏｒｆｆ容度与 Ｈａｕｓｄｏｒｆｆ测度相等的集的充分必要条件．对于满足开集条件的自相似集，验证了它的Ｈａｕｓｄｏｒｆｆ容度与Ｈａｕｓｄｏｒｆ测度相等并给出了它的Ｈａｕｓｄｏｒｆｆ测度的一个便于应用的公式．作为例子，给出了均匀康托集的Ｈａｕｓｄｏｒｆｆ测度的一种新的计算方法，对于Ｋｏｃｈ曲线的Ｈａｕｓｄｏｒｆｆ测度的上限也作了讨论．
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| 关 键 词： | 容度 测度 维数 开集条件 自相似集 |
| 文章编号： | 0583-1431(2001)01-0117-08 |
| 修稿时间： | 1998年11月30 |
On Hausdorff Measures of Self-Similar Sets |
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| Institution: | WEN Sheng You (Department of Mathematics, Hanshan Teacher's College, Chaozhou 521041, P. R. China) (Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China) XU Shao Yuan (Department of Mathematics, Huaibei Coal Industry Teacher's College, |
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| Abstract: | Some sufficient and necessary conditions for sets having the same Hausdorff content and Hausdorff measure are obtained. For the self-similar set satisfying the open set condition, it is proved that its Hausdorff content and Hausdorff measure are equal and a formula, which is convenient for use, of its Hausdorff measure is given. As applications, the Hausdorff measures of uniform Cantor sets are computed in a new way and the upper bound problem of the Hausdorff measure of the Koch curve is also discussed. |
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| Keywords: | Content Measure Dimension Open set condition Self-similar sets |
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