Conditional expectation of Pettis integrable random sets: existence and convergence theorems

被引：0
|
作者：
M. El Allali
F. Ezzaki
机构：
[1] University Sidi Mohamed Ben Abdellah,Faculty of Sciences and Technologies, Laboratory of Modeling and Mathematical Structures
来源：
Advances in Operator Theory | 2021年 / 6卷
关键词：
Pettis integration; Random sets; Conditional expectation; Fatou’s lemma; Monotone convergence theorem; Linear topology; 46G12; 60G42; 60G46;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Existence of the conditional expectation of Pettis integrable random sets is proved. A Representation theorem of Pettis integrable set-valued regular martingales by regular martingales selectors is provided. As applications, Levy’s theorem convergence results are studied for Pettis integrable random sets. At the end of this paper, monotone convergence theorem and Fatou’s lemma are established for a sequence of conditional expectations of Pettis integrable random sets.
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