Convergence theorems for set-valued conditional expectations

Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 1, page 97-104
  • ISSN: 0010-2628

Abstract

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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 σ -fields.

How to cite

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Papageorgiou, Nikolaos S.. "Convergence theorems for set-valued conditional expectations." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 97-104. <http://eudml.org/doc/247504>.

@article{Papageorgiou1993,
abstract = {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.},
author = {Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {measurable multifunction; set-valued conditional expectation; Levy's theorem; support function; Kuratowski-Mosco convergence of sets; Kuratowski-Mosco convergence; random set; convergence theorems; set- valued conditional expectations; integrable selectors},
language = {eng},
number = {1},
pages = {97-104},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Convergence theorems for set-valued conditional expectations},
url = {http://eudml.org/doc/247504},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
TI - Convergence theorems for set-valued conditional expectations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 97
EP - 104
AB - 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.
LA - eng
KW - measurable multifunction; set-valued conditional expectation; Levy's theorem; support function; Kuratowski-Mosco convergence of sets; Kuratowski-Mosco convergence; random set; convergence theorems; set- valued conditional expectations; integrable selectors
UR - http://eudml.org/doc/247504
ER -

References

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