| 均匀三部分康托集的Hausdorff中心测度 |
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| 引用本文： | 戴美凤,阮火军,苏维宜.均匀三部分康托集的Hausdorff中心测度[J].数学学报,2006,49(1):11-18. |
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| 作者姓名： | 戴美凤 阮火军 苏维宜 |
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| 作者单位： | [1]江苏大学理学院数学系,镇江212013 [2]浙江大学数学系,杭州310027 [3]南京大学数学系,南京210093 |
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| 摘 要： | 均匀三部分康托集K(λ,3)是满足开集条件的自相似分形集．本文通过一个概率测度μ在点x的上球密度的计算给出了K(λ,3)的s维Hausdorff中心测度的精确值,其中s=logλ1/3是K(λ,3)的Hausdorff维数．
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| 关 键 词： | 均匀三部分康托集 Hausdorff中心测度 迭代函数系 |
| 文章编号： | 0583-1431（2006）01-0011-08 |
| 收稿时间： | 2004-04-29 |
| 修稿时间： | 2004-04-292004-09-15 |
Hausdorff Centered Measure of Uniform 3-part Cantor Set |
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| Mei Feng DAI,Huo Jun RUAN,Wei Yi SU.Hausdorff Centered Measure of Uniform 3-part Cantor Set[J].Acta Mathematica Sinica,2006,49(1):11-18. |
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| Authors: | Mei Feng DAI Huo Jun RUAN Wei Yi SU |
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| Institution: | Mei Feng DAI Department of Mathematics, Jiangsu University, Zhenjiang 212013, P. R. China Huo Jun RUAN Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China Wei Yi SU Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China |
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| Abstract: | The uniform 3-part Cantor set K(λ, 3) is a self-similar fractal set satisfying the open set condition. In this paper, the exact value of the s-dimensional Hausdorff centered measure of K(λ,3) is given by computing the upper spherical density of a probability measure μ at point x, where s = logλ1/3 is the Hausdorff dimension of K(λ,3). |
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| Keywords: | Hausdorff centered measure uniform 3-part Cantor set iterated function systems |
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