| 重分形Hausdorff测度的有限测度子集 |
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| 引用本文： | 黄立虎,余旌胡. 重分形Hausdorff测度的有限测度子集[J]. 数学研究及应用, 2000, 20(2): 166-170 |
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| 作者姓名： | 黄立虎 余旌胡 |
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| 作者单位： | 1. 中国人民大学统计系,北京 100872
2. 中国科学院武汉物理与数学研究所,430071 |
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| 摘 要： | 设μ为 Ｒd上 Ｂｏｒｅｌ概率测度，ｑ，ｔ∈Ｒ，记 Ｈμq,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度，证明了当μ为测度时，Ｈμq,t的有限测度子集存在．
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| 关 键 词： | 重分形Hausdorff测度 有限测度子集 概率测度 |
| 文章编号： | 1000-341(2000)02-0166-05 |
| 收稿时间： | 1997-07-18 |
| 修稿时间： | 1997-07-18 |
Subsets with Finite Measure of Multifractal Hausdorff Measures |
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| HUANG Li-hu and YU Jing-hu. Subsets with Finite Measure of Multifractal Hausdorff Measures[J]. Journal of Mathematical Research with Applications, 2000, 20(2): 166-170 |
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| Authors: | HUANG Li-hu and YU Jing-hu |
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| Affiliation: | Dept. of Stat; Renmin University of China; Beijing 100872;Wuhan Inst. of Phy and Math; The Chinese Academy of Sciences |
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| Abstract: | Let μ be a Borel Probability measure on Rd. q, t, ∈ R. Let Hq,tμ denote the multifractal Hausdorff measure. We prove that, when μ satisfies the so-called Federer condition, for a closed subset E ∈ Rn, such that Hq,tμ(E) ＞ 0 , there exists a compact subset F of E with 0 ＜ Hq,tμ(F) ＜∞, i.e., the finite measure subsets of multifractal Hausdorff measure exist. |
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| Keywords: | multifractal Hausdorff measure finite measure subset net measure. |
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