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Hausdorff dimension and measure of a class of subsets of the general Sierpinski carpets |
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| Authors: | Yong Xin Gui |
| Affiliation: | 1. Department of Mathematics, Xianning College, Xianning, 437100, P. R. China 2. Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China |
| Abstract: | In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions 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 and finite. |
| Keywords: | the general Sierpinski carpets Hausdorff dimension Hausdorff measure |
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