Geodesic
Convergence theorems for set-valued conditional expectations
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 97-104
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In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy's martingale convergence theorem, while the second involves a nonmonotone sequence of sub $\sigma $-fields.
In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy's martingale convergence theorem, while the second involves a nonmonotone sequence of sub $\sigma $-fields.
Classification : 28B20, 60D05, 60F99, 60G48, 60G99
Keywords: measurable multifunction; set-valued conditional expectation; Levy's theorem; support function; Kuratowski-Mosco convergence of sets 
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     author = {Papageorgiou, Nikolaos S.},
     title = {Convergence theorems for set-valued conditional expectations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {97--104},
     year = {1993},
     volume = {34},
     number = {1},
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     zbl = {0788.60021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993_34_1_a10/}
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Papageorgiou, Nikolaos S. Convergence theorems for set-valued conditional expectations. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 97-104. http://geodesic.mathdoc.fr/item/CMUC_1993_34_1_a10/