摘要
系统地评介有关随机递归集的概率性质,包括收敛性及可测性;分布的0-1 律及支撑.对各类自相似性作了较详细的评介.Hutchinson 构造了一类严自相似集,并得到了许多重要的分形性质.Graf研究了一个特殊的统计自相似集的分形性质. 本文研究了各种自相似集的概率性质与分形性质.
We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;
出处
《武汉大学学报(自然科学版)》
CSCD
1999年第5期577-580,共4页
Journal of Wuhan University(Natural Science Edition)
基金
国家自然科学基金
国家教委博士点基金
关键词
随机递归集
统计自相似性
确切测度函数
H维数
random recursive set, statistically self-similar set, Hausdorff dimension, exact measure function