统计自相似集与随机不变测度

Statistically Self-Similar Sets and Random Lnvariant Measures

设 X是一完备可分度量空间 ,K(ω)为 Graf随机模型下的随机递归集 .该文构造了一列随机不变测度 μ*n (n≥ 1 ) ,它们是 H utchinson确定模型下不变测度的推广 ;证明了存在一随机概率测度 μ*,使得 Suppμ*=K(ω)且 μ*n → μ*(n→∞ ) (弱收敛 ) ;得到了 μ*n

Let \$X\$ be a complete separable metric space and \$K(ω)\$ be the statistically self-similar sets defined by Graf. In this paper, we construet a series of random invariant measures \$U\+*\-n(n≥1),\$ which are the generalizations of invariant measures stuided by Hutchinson and prove that there exists a probability measure \$U\+*\$ with supp\$U\+*=K(ω)\$ sueh that \$U\+*\-n→U\+*\$(weakly), finally, we obtain some local properties of \$U\+*\-n\$.