Gauge integrals and series
This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.
Generalisations of -density
Generalizations of Castaing's theorem on selectors
Generalized Herglotz theorem in vector lattices
Generalized Lusin sets with the Blackwell property
Generalizing Hopf and Lax-Oleinik Formulae via Conjugate Integral.
Geometric decomposability properties of probability measures
Group valued, α-additive set functions
Group-valued measures on coarse-grained quantum logics
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...
Henstock-Kurzweil and McShane product integration; descriptive definitions
The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function is absolutely continuous. As a consequence we obtain that the McShane product integral of over exists and is invertible if and only if is Bochner integrable...
Hilbert-space-valued measures on Boolean algebras (extensions).
Hilbert-space-valued states on quantum logics
H-regularidad para medidas vectoriales.
Ideal convergence and divergence of nets in -groups
In this paper we introduce the - and -convergence and divergence of nets in -groups. We prove some theorems relating different types of convergence/divergence for nets in -group setting, in relation with ideals. We consider both order and -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that -convergence/divergence implies -convergence/divergence for every ideal, admissible for...
Implicit Markov kernels in probability theory
Having Polish spaces , and we shall discuss the existence of an -valued random vector such that its conditional distributions satisfy or for some maps , or multifunction respectively. The problem is equivalent to the existence of universally measurable Markov kernel defined implicitly by or respectively. In the paper we shall provide sufficient conditions for the existence of the desired Markov kernel. We shall discuss some special solutions of the - or -problem and illustrate...
Individual ergodic theorem in a regular space
Inequalities for product operators and vector valued ergodic theorems
Integrability for the Dobrakov integral
Integración de funciones con valores en un espacio localmente convexo respecto de medidas infinitas. II.
Integración de funciones con valores en un espacio localmente convexo respecto de medidas infinitas. III.