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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 ℬ n X n where ( ℬ 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.

Decomposable sets and Musielak-Orlicz spaces of multifunctions

Andrzej Kasperski (2005)

Banach Center Publications

We introduce the Musielak-Orlicz space of multifunctions X m , φ and the set S F φ of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to X m , φ . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space X m , φ and the set S F φ .

Differential inclusions and multivalued integrals

Kinga Cichoń, Mieczysław Cichoń, Bianca Satco (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...

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