| Rd上一个随机剪切集的Hausdorff维数 |
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| 引用本文： | 朱,志,勇.Rd上一个随机剪切集的Hausdorff维数[J].华中师范大学学报(自然科学版),2012,46(1):9-13. |
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| 作者姓名： | 朱 志 勇 |
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| 作者单位： | 西北农林科技大学理学院,陕西杨凌,712100 |
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| 摘 要： | 通过把随机集上的随机测度定义为与分形结构相关联的随机测度序列的极限,使用鞅方法讨论了Rd上一个随机剪切集的Hausdorff维数,获得直线上一个随机剪切集的Hausdorff维数结果在高维空间上的一个推广.
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| 关 键 词： | 分形 随机分形 随机剪切集 随机测度 Hausdorff维数 |
Hausdorff dimension of a random cut-out set in Rd |
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| ZHU Zhiyong.Hausdorff dimension of a random cut-out set in Rd[J].Journal of Central China Normal University(Natural Sciences),2012,46(1):9-13. |
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| Authors: | ZHU Zhiyong |
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| Institution: | ZHU Zhiyong(College of Science,Northwest A & F University,Yangling,Shanxi 712100) |
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| Abstract: | In this paper,we discuss Hausdorff dimension of a random cut-out set in Rd by using martingale techniques: the usual procedure is to define a random measure on the random set as the limit of a sequence of random measures associated with the construction,and to use martingales to deduce properties of the limiting measure,and to obtain a generalization of the results of a random cut-out set on the line. |
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| Keywords: | fractal random fractal random measure random cut-out set Hausdorff dimension |
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