一类统计自相似集的重分形分解

Multifractal Decomposition of a Class of Statistically Self-similar Sets

将余旌胡和胡迪鹤所研究的统计自相似集K(ω)的限制条件放宽,利用Arbeiter与Patzschke的思想,构造了两个鞅,最终给出了在强开集条件下K(ω)的重分形分解集Kα(ω)关于支撑在K(ω)上的随机测度νq,ω的Hausdorff维数表达式.

In this paper, we generalize the statistically self-similar set K（w） proposed by Yu Jinghu and Hu Dihe, construct two martingles by making use of the idea from Arbeiter and Patzschke, and obtain the Hausdorff dimensional expression of the multifractal decomposition sets Ka（w） of K（w） for the random measure Vq,w which is supported by K（w） under the strong open set condition.