Characterization of strongly exposed points in .
Classical hierarchies from a modern standpoint. Part I. C-sets
CM-selectors for pairs of oppositely semicontinuous multifunctions and some applications to strongly nonlinear inclusions.
Compactness and convergence of set-valued measures
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.
Connections between recent Olech-type lemmas and Visintin's theorem
A recent Olech-type lemma of Artstein-Rzeżuchowski [2] and its generalization in [7] are shown to follow from Visintin's theorem, by exploiting a well-known property of extreme points of the integral of a multifunction.
Continuity properties of solutions of multivalued equations with white noise perturbation.
Continuous selection theorems
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
Continuous selections for a class of non-convex multivalued maps
Convergence of conditional expectations for unbounded closed convex random sets
We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form where is a decreasing sequence of sub-σ-algebras and is a sequence of closed convex random sets in a separable Banach space.
Convergence theorems for Banach space valued integrable multifunctions.
Convergence theorems for set-valued conditional expectations
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 -fields.
Correction on “The properties of the Aumann integral with applications to differential inclusions and control systems”
Correspondence between subadditive integrals and small systems
Decomposable sets and Musielak-Orlicz spaces of multifunctions
We introduce the Musielak-Orlicz space of multifunctions and the set of φ-integrable selections of F. We show that some decomposable sets in Musielak-Orlicz space belong to . We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space and the set .
Differential inclusions and multivalued integrals
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...
Equilibrium points of random generalized games.
Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces
Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in are considered. Techniques used here are inspired by [3].
Errata to the paper: ``Regularization of closed-valued multifunctions in a non-metric setting''
Existence of equilibria in finitely additive nonatomic coalition production economies.
Existence of measurable selectors and parametrizations for -valued multifunctions