| Hausdorff测度的等价定义 |
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| 引用本文： | 陆式盘,郑振容.Hausdorff测度的等价定义[J].集美大学学报(自然科学版),1998,3(3):15-20. |
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| 作者姓名： | 陆式盘 郑振容 |
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| 作者单位： | 集美大学师范学院!厦门，361021 |
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| 基金项目： | 集美大学师范学院科研基金 |
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| 摘 要： | Thomson1]与Edgar2]曾给出Hausdorff测度的等价定义。在他们的工作基础上，又补充了另外的等价定义，并改进他们的等价性证明。作为应用，改进并完善了3]中的命题4．9的证明，进而可以较为简单求出一般Cantor集的Hausdorff测度。
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| 关 键 词： | Hausdorff维数 Hausdorff测度 |
The Equivalent Definitions of Hausdorff Measure |
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| Lu Shipan,Zheng Zhenrong,Lin Yingjian.The Equivalent Definitions of Hausdorff Measure[J].the Editorial Board of Jimei University(Natural Science),1998,3(3):15-20. |
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| Authors: | Lu Shipan Zheng Zhenrong Lin Yingjian |
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| Abstract: | In this paper we shall introduce a new definition of the Hausdorff measure, which is based on the study of Thomson1] and Edgar2], and give an equivalent proof among the three definitions of Hausdorff measure. As an application, we improve the proof of the proposition 4.9 in3],and then we can evaluate the Hausdorff measure of a general Cantor set more easily. |
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| Keywords: | Hausdorff dimension Hausdorff measure |
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