随机递归集研究的新进展（Ⅰ）

随机递归集研究的新进展（Ⅰ） The Advances of the Research for Random Recursive Sets（Ⅰ） 胡迪鹤 HU Di\|he 1 first-author 武汉大学数学与计算机科学学院,武汉,430072 武汉大学数学与计算机科学学院,武汉,430072 College of Mathematics and Computer Science, Wuhan University,Wuhan 430072, China) \ College of Mathematics and Computer Science, Wuhan University,Wuhan 430072, China) \ 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.\; 随机递归集 统计自相似性 Hausdorff维数 确切测度函数 random recursive set statistically self-similar set Hausdorff dimension exact measure function O211 国家自然科学基金(61672102);国家教委博士点基金 1999-05-01 2021-04-01 5