随机递归集研究的新进展(Ⅰ)

The Advances of the Research for Random Recursive Sets(Ⅰ)

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.\;