Banach格中的本性收敛、O-收敛及随机收敛

Banach格中的本性收敛、O-收敛及随机收敛 ESSENTIAL CONVERGRNCE O-CONVERGENCE AND STOCHASTIC CONVERGENCE IN BANACH LATTICE 胡晓予 Hu Xiaoyu 1 first-author 武汉大学数学系 85级研究生 武汉大学数学系 85级研究生 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University Neveu在1975年研究过定向集上实值随机过程的本性收敛性;Egghe在1984年研究过取值于Banach格的上、下鞅序列的收敛性。而本文为研究定向集上的取值于Banach格的随机过程的收敛性作准备,首先给出了Banach格中本性收敛的概念以及本性上、下确界的存在唯一性定理,还研究了关于本性收敛、O-收敛与随机收敛的关系,Banach格中的各种积分收敛定理。 This paper gives us the definition of essential convergence in Banach lattice and proves the existence and uniqueness of essential supremum and essential infimum therom, based on it, the paper also investigates the relations among essential convergence, stochastic convergence, and O-convergence, then it proves the Faton lemma, monotone convergence therom and bounded convergence therom in Banach lattice. For the completeness, this paper contains some former resultce. 巴拿赫格 定向集 本性收敛 随机收敛 O-收敛 鞅 Banach lattice directed set essential convergence stochastic convergence O convergence Martingale. 国家教委科学基金 1989-01-01 2021-04-01 1