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The Hausdorff dimension of sets related to the general Sierpinski carpets |
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| Authors: | Yong Xin Gui Wen Xia Li |
| Affiliation: | 1. Department of Mathematics, East China Normal University, Shanghai, 200241, P. R. China 2. Department of Mathematics, Xianning College, Xianning, 437005, P. R. China 3. Department of Mathematics, East China Normal University, Shanghai, 200241, P. R. China |
| Abstract: | In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the Hausdorff and box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite. |
| Keywords: | general Sierpinski carpets Hausdorff dimension Hausdorff measure |
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