集值条件期望的收敛定理

Convergence Theorems for Set-valued Conditional Expectations

  • 摘要: 本文给出了集合序列弱极限的表示定理,得到了随机集列关于σ-域流的条件期望序列在弱收敛意义下的Fatou型引理和控制收敛定理.

     

    Abstract: In this paper, a representation theorem is given for the weak limit of a sequence of sets in a Banach space. We obtain Fatou’s lemmas and dominated convergence theorems for set-valued conditional expectations with an increasing sequence of σ-fields.

     

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