A Note on Hausdorff Measures of Sierpinski Carpets |
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| Authors: | Ma Dongkui Xu Zhiting |
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| Institution: | 1. Department of Applied Mathematics, South China University of Technology, Guangzhou, 510640, P R China
2. Department of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510090, P R China
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| Abstract: | In this paper, regular Sierpinski carpet as a new concept is given. The exact value of Hausdorff measure of the regular Sierpinski carpet and the range of Hausdorff measures for all forms of generalized Sierpinski carpets is also obtained. For any one of the generalized Sierpinski carpets we show that there exists a regular carpet such that they have the same Hausdorff measures. |
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