DECIMAL SET WITH ZERO MEASURE AND FULL HAUSDORFF DIMENSION |
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| Authors: | Xu Ning Su Weiyi Dept of Math Naning Normal University Naning PRCDept of Math Naning University Naning PRC |
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| Institution: | Dept.of Math., Nanjing Normal University, Nanjing 210097, PRC;Dept.of Math., Nanjing University, Nanjing 210093, RC |
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| Abstract: | LetFλ ={x∈ (0,1){2nx} ≥1/2k,n∈ z+}, z++ = {0,1,2,3,...}, k∈ N;F = U∞k=1Fλ be a decimal set in (0, 1), where {2nx} is the fractional part of a number 2nx. In this note, we prove that dirnнF = 1 and Н1(F) = 0, where dimн is Hausdr off dimension, and Н1(F) is the Hausdorff measure of F. |
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| Keywords: | Hausdr off Dimension Recursive Graph Set Eigenvalues |
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