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Compactness and convergence of set-valued measures

Kenny Koffi Siggini (2009)

Colloquium Mathematicae

We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.

Continuous selection theorems

Michał Kisielewicz (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.

Convergence of conditional expectations for unbounded closed convex random sets

Charles Castaing, Fatima Ezzaki, Christian Hess (1997)

Studia Mathematica

We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form E n X n where ( n ) is a decreasing sequence of sub-σ-algebras and ( X n ) is a sequence of closed convex random sets in a separable Banach space.

Convergence theorems for set-valued conditional expectations

Nikolaos S. Papageorgiou (1993)

Commentationes Mathematicae Universitatis Carolinae

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.

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