双条件期望的收敛定理及不等式

双条件期望的收敛定理及不等式 Convergence Theorems and Inequalities of Double Conditional Expectation 邱育锋 QIU Yu-feng~1 1 2 3 first-author 胡迪鹤 HU Di-he~2 1 2 3 龙岩学院数学系 龙岩学院数学系 Department of Mathematics, Longyan College Department of Mathematics, Longyan College 武汉大学数学与统计学院,福建,龙岩,364000 武汉大学数学与统计学院,福建,龙岩,364000 College of Mathematics and Statistics, Wuhan University College of Mathematics and Statistics, Wuhan University ,湖北,武汉,430072 ,湖北,武汉,430072 引进了B值随机变量及可测集Γ的双条件期望的概念,研究了双条件期望的主要性质,得到了双条件期望下的几个重要不等式,进而证明了双条件期望的有关收敛定理. The concept of double conditional expectation for B-valued random variable and measurable set Γ is introduced. We investigate the properties of the related double conditional expectation and obtained several important inequalities. Furthermore the convergence theorems with respect to double conditional expectation are proved. 双条件期望 收敛定理 不等式 强可测随机元 double conditional expectation convergence theorem inequality strongly measurable random element O211.6 国家自然科学基金资助项目（10371092）;武汉大学基金资助项目 2005-01-01 2021-04-01 1