Compactness properties of the integration mapassociated with a vector measure
Compactness properties of vector-valued integration maps in locally convex spaces
Compositions of operators with vector valued maps
Conical measures and properties of a vector measure determined by its range
We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...
Conical measures and vector measures
Every conical measure on a weak complete space is represented as integration with respect to a -additive measure on the cylindrical -algebra in . The connection between conical measures on and -valued measures gives then some sufficient conditions for the representing measure to be finite.
Connectedness properties of the range of vector and semimeasures.
Continuous additive mappings
Continuous extensions of spectral measures
Continuous linear functionals on the space of Borel vector measures
We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on...
Continuous selections for a class of non-convex multivalued maps
Control and separating points of modular functions
Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on -dimensional compact intervals
In this paper we use a generalized version of absolute continuity defined by J. Kurzweil, J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exch. 17 (1992), 110–139. By applying uniformly this generalized version of absolute continuity to the primitives of the Henstock-Kurzweil-Pettis integrable functions, we obtain controlled convergence theorems for the Henstock-Kurzweil-Pettis integral. First, we present a controlled convergence theorem for...
Convergence of Banach lattice valued stochastic processes without the Radon-Nikodym property.
Convergence theorems for Banach space valued integrable multifunctions.
Convergence theorems for the Birkhoff integral
We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence of functions from a measure space to a Banach space. In one result the equi-integrability of ’s is involved and we assume almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of to is assumed.
Convolutions and products of partially ordered vector-valued positive measures.
Convolutions with the continuous primitive integral.
Copies of in the space of Pettis integrable functions with integrals of finite variation
Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. We show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of if and only if X does.
Correction to: Integrating bounded functions for the Dobrakov integral
Correction to the paper ’Copies of in the space of Pettis integrable functions with integrals of finite variation’ (Studia Math. 210 (2012), 93-98)