| Sierpinski地毯的Hausdorff测度的一个估计 |
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| 引用本文： | 王春勇,李雄.Sierpinski地毯的Hausdorff测度的一个估计[J].太原师范学院学报(自然科学版),2008,7(1):1-4. |
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| 作者姓名： | 王春勇 李雄 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西,西安,710062 |
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| 摘 要： | 目的：对一种Sierpinski地毯进行Hausdorff测度的上限估计.方法：推广Hausdorff测度的次可数可加性,并利用Sierpinski地毯的对称性,改进文献1]中的覆盖.结果文献1]得到上限估计H^s（S）≤1.409 736 1,经改进后得到H^s（S）≤1.396 434 226 4.结论：Hausdorff测度的次可数可加性的推广以及对称性可以应用于研究其他一些分形集的情形.
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| 关 键 词： | Sierpinski地毯 Hausdorff测度 Hausdorff维数 覆盖 |
Estimating the Hausdorff Measure of a Sierpinski Carpet |
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| Wang Chunyong,Li Xiong.Estimating the Hausdorff Measure of a Sierpinski Carpet[J].Journal of Taiyuan Normal University:Natural Science Edition,2008,7(1):1-4. |
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| Authors: | Wang Chunyong Li Xiong |
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| Institution: | Wand Chunyong Li Xiong(College of Mathematics and Information Science,Shaanxi Normal University,Xi＇an 710062,China) |
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| Abstract: | Aim for a special type of sierpinski carpet,we try to obtain the estimate value of the upper limit of its hausdorff measure.Methods by generalizing the countable subadditivity of hausdorff measure and using the symmetry of the sierpinski carpet,the author improves a coving of sierpinski carpet in literature^1].Results in literature^1],the estimate value of the upper limit is1.4097361,we improves it and gets.Conclusion The generalization of the countable subadditivity of hausdorff measure and the symmetry can be used in some other fractal set. |
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| Keywords: | sierpinski carpet hausdorff measure hausdorff dimension covering |
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