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摘要: C为三分康托集, 考虑何时交集C\cap (C+t)\cap (C+s) 非空, 计算出当交集非空时 (t,s) 的 Hausdorff 维数. 证明了: 对于平面上几乎处处的(t,s), dim_H C\cap (C+t)\cap (C+s)=0. 利用Moran集的相关结论得到当交集非空时dim_H C\cap (C+t)\cap (C+s)的表达式.Abstract: Let C be the Cantor ternary set. The condition of the intersection C\cap (C+t)\cap (C+s)\neq\emptyset was considered and the Hausdorff dimension of (t,s) was computed when the intersection was nonempty. A conclusion was proved: dim_H C\cap (C+t)\cap (C+s)=0 for a.e. (t,s)\in{\bf R}\times {\bf R}. Then by a related result of Moran set, the expression of dim_H C\cap (C+t)\cap (C+s) was investigated.
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Key words:
- Cantor ternary setintersectionend-pointsMoran sets /
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