Radon-Nikodym derivatives in vector integration
Radon-Nikodym property
For a Banach space and a probability space , a new proof is given that a measure , with , has RN derivative with respect to iff there is a compact or a weakly compact such that is a finite valued countably additive measure. Here we define where is a finite disjoint collection of elements from , each contained in , and satisfies . Then the result is extended to the case when is a Frechet space.
Radon-Nikodym property for vector-valued integrable functions
It is proved that if a Frechet space has property, then also has property, for .
Regularity conditions and absolute continuity for vector measures.
Relaxation for a class of nonconvex functionals defined on measures
Remarks on the integrability in Banach spaces
Représentation intégrale dans des sous-espaces de fonctions à valeurs vectorielles
Representation of Itô integrals by Lebesgue/Bochner integrals
In [Yong 2004], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later...
Representation of multilinear operators on
Representation of multilinear operators on C(K, X) spaces.
We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.
Representation of operators by bilinear integrals
Representation of operators with martingales and the Radon-Nikodým property.
The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded...
Representation of vector measures.
Reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces.
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Riesz spaces valued measures and processes