Existence of weak Radon-Nikodým derivatives for set-valued measures and conditional expectations for weak set-valued random variables. (Q2739183)
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scientific article; zbMATH DE number 1643593
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of weak Radon-Nikodým derivatives for set-valued measures and conditional expectations for weak set-valued random variables. |
scientific article; zbMATH DE number 1643593 |
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2001
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weak Radon-Nikodým derivatives
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set-valued measures
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Existence of weak Radon-Nikodým derivatives for set-valued measures and conditional expectations for weak set-valued random variables. (English)
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In this paper, the authors give the necessary and sufficient conditions for existence of weak Radon-Nikodým derivatives for set-valued measures. They also obtain the characteristics of random variables with weakly compact convex set-values when they have conditional expectations. Note that the existence of Radon-Nikodým derivatives of closed set-valued measures has been developed in [\textit{Q. Duan, W. Zhang} and \textit{Z. Nie}, Acta Math. Appl. Sin. 19, 571--575 (1996; Zbl 1019.28500)].
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