On measures and integrals with values in ordered groups
On multivalued martingales, multimeasures and multivalued Radon-Nikodym property
In this paper we prove a representation result for essentially bounded multivalued martingales with nonempty closed convex and bounded values in a real separable Banach space. Then we turn our attention to the interplay between multimeasures and multivalued Riesz representations. Finally, we give the multivalued Radon-Nikodym property.
On Pettis integrability
Assuming that is a complete probability space and a Banach space, in this paper we investigate the problem of the -inheritance of certain copies of or in the linear space of all [classes of] -valued -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.
On Pettis integrals with separable range
Several techniques have been developed to study Pettis integrability of weakly measurable functions with values in Banach spaces. As shown by M. Talagrand [Ta], it is fruitful to regard a weakly measurable mapping as a pointwise compact set of measurable functions - its Pettis integrability is then a purely measure-theoretic question of an appropriate continuity of a measure. On the other hand, properties of weakly measurable functions can be translated into the language of topological measure theory...
On random variables having values in a vector lattice
On Riemann integration of functions with values in topological linear spaces
On second derivates of convex functions.
On selections of multifunctions
The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.
On set-valued cone absolutely summing maps
Spaces of cone absolutely summing maps are generalizations of Bochner spaces L p(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L 1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of , and to derive necessary...
On Some Classes of Operators on C(K,X)
Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T:C(K,X) → Y is a strongly bounded operator with representing measure m:Σ → L(X,Y). We show that if T is a strongly bounded operator and T̂:B(K,X) → Y is its extension, then T is limited if and only if its extension T̂ is limited, and that T* is completely continuous (resp. unconditionally...
On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras [Book]
On some mappings generating vector -measures
On Stone-type extensions for group-valued measures
On strongly additive set functions
On strongly Pettis integrable functions in locally convex spaces.
Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is integrable...
On superpositional measurability of semi-Carathéodory multifunctions
It is shown that product weakly measurable lower weak semi-Carathéodory multifunction is superpositionally measurable.
On superpositionally measurable multifunctions
On superpositionally measurable semi-Carathéodory multifunctions
For multifunctions , measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.
On systems of null sets
The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.
On the cliquish, quasicontinuous and measurable selections
The purpose of this paper is the investigation of the necessary and sufficient conditions under which a given multifunctions admits a cliquish and measurable selection. Our investigation also covers the search for quasicontinuous selections for multifunctions which are continuous with respect to the generalized notion of the semi-quasicontinuity.