随机不变测度的维数与维数分布

介绍了测度的维数和维数分布的概念，对随机不变测度μ^*，获得了μ^*的维数及其维数分布。     

The construction of statistically self-similar measures

We have studied statistically self-similar measures together with statistically self-similar sets in this paper. A special kind of statistically self-similar measures has been constructed and a class of statistically self-similar sets as well. Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China Hu Dihe: born in May 1935, Professor     

统计自相似集上概率测度量子化维数的一些计算

给出了统计自相似集上概率测度的量子化维数一些具体例子的计算.     

一类统计自相似集的重分形分解

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.     

双Lipschitz条件下自相似测度的维数估计

给出了强开集条件和双Lipschitz条件下自相似测度的Hausdorff维数的上下界估计．我们通过对吸引子的局部性质的研究，给出了对吸引子的点态维数的估计。从而得到了本文的主要结果．     

The convergence of statistically self-similar sets and the upper bound and lower bound of Hausdorff measure

We constructed a class of self-similar sets and proved the convergence in this paper. Besides these, the upper bound and lower bound of Hausdorff measures of them were given too. Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China Hu Dihe: born in May 1935, Professor     

概率空间上的盒维数

在概率空间（Ω,ξ,μ）上定义关于卢的上、下盒维数,并给出了上、下盒维数的另一等价定义,讨论了概率空间上关于产的上、下盒维数与关于μ的Hausdorff维数、预填充维数及填充维数之间的关系．     

统计自相似集与随机不变测度

研究了统计自相似集K(w)的结构,定义了随机不变测度μ^*,讨论了μ^*的性质,得到了μ^*的支撑。