| 一类长方形sierpinski垫片的Hausdorff测度与上凸密度 |
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| 引用本文： | 许荣飞. 一类长方形sierpinski垫片的Hausdorff测度与上凸密度[J]. 科学技术与工程, 2010, 10(2) |
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| 作者姓名： | 许荣飞 |
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| 作者单位： | 南京师范大学泰州学院数学系,泰州,225300 |
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| 摘 要： | 在平面上,由长为1,宽为a[1/2≤a≤1]的长方形生成的一类自相似集,也就是一个Sierpinski垫片。在满足强分离条件及维数小于1的条件下,证明了自然覆盖为其实现上凸密度1计算的最好形状,自然覆盖即是最好的覆盖。作为它的直接推论,可以得到该类自相似集的Hausdorff测度的精确值。
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| 关 键 词： | 长方形Hausdorff测度 自相似集 上凸密度 |
| 收稿时间： | 2009-10-01 |
| 修稿时间： | 2009-10-01 |
The Hausdorff measure of a class of self-similar sets of a class of sierpinski carpet of rectangular |
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| XuRongfei. The Hausdorff measure of a class of self-similar sets of a class of sierpinski carpet of rectangular[J]. Science Technology and Engineering, 2010, 10(2) |
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| Authors: | XuRongfei |
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| Affiliation: | Department of Mathmatics Taizhou College Nanjing Normal University/a>;Taizhou 225300/a>;P.R.China |
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| Abstract: | The exact computation of Hausdorff measure of a class of self-similar sets on the plane is deal with.Under some condition,the natural covering is the best one,and the Hausdorff measure of those sets are equal to1+a2s,where s is its Hausdorff dimension. |
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| Keywords: | rectangular Hausdorff measure self-similar sets upper convex density |
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