| m分Cantor尘的Hausdorff测度 |
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| 引用本文： | 曾超益,袁德辉.m分Cantor尘的Hausdorff测度[J].纯粹数学与应用数学,2009,25(2):356-362. |
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| 作者姓名： | 曾超益 袁德辉 |
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| 作者单位： | 韩山师范学院数学与信息技术系,广东,潮州,521041 |
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| 基金项目： | 广东省教育科研课题，江西省自然科学基金项目 |
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| 摘 要： | 为得到一类相似分形的Hausdorff测度准确值．给出了m分Cantor尘的几何结构，利用几何度量关系对m分Cantor尘的Hausdorff测度准确值进行研究．证明了m分Cantor尘的Hausdorff测度准确为H^s（E）=1/（m-1）^s（m-2k＋1）^2＋（m-1）^2]^s/2,其中s=logm4，m≥4，1≤k≤m．结果表明它是Cantor尘和Sierpinski地毯的Hausdorff测度的准确值的推广，4分Cantor尘和4分Sierpinski地毯的Hausdorff测度的准确值是其特例．
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| 关 键 词： | 相似分形 m分Cantor尘 Hausdorff测度 p级拷贝 |
Hausdorff measure of m-Cantor Dust |
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| ZENG Chao-yi,YUAN De-hui.Hausdorff measure of m-Cantor Dust[J].Pure and Applied Mathematics,2009,25(2):356-362. |
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| Authors: | ZENG Chao-yi YUAN De-hui |
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| Institution: | ZENG Chao-yi,YUAN De-hui (Department of Mathematics,Hanshan Normal University,Chaozhou 710071,China) |
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| Abstract: | To obtain the exact Hausdorff measure value of a kind of m-Cantor dust. We present the geometry construction and discuss the exact Hausdorff measure of this kind of m-Cantor dust. Proving the theorem that the exact value of m-Cantor dust is H^s（E）=1/（m-1）^s（m-2k＋1）^2＋（m-1）^2]^s/2, where s = logm 4, m ≥ 4,1 ≤ k ≤ m, through geometric metric relation. According the properties of similar fractal geometry, we obtain the exact Hausdorff measure value of a kind of m-Cantor dust, which is extension about the exact Hausdorff measure value of 4-Cantor dust and 4-Sierpinski carpet. |
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| Keywords: | Hausdorff measure similar fractal m-Cantor dust p-copy |
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