Integral extension procedures in weakly σ-complete lattice-ordered groups, II
Integral extension procedures in weakly σ-complete lattice-ordered groups, I
Integralerweiterung durch Integralnormen mit Werten in prägeordneten Halbgruppen.
Intégration dans certains espaces de Riesz à distance concave
Integration in partially ordered linear spaces
Konvergenzsaetze fur ein voll Daniell-integral
Lattice-valued Borel measures. III.
Let be a completely regular space, a boundedly complete vector lattice,
Measurability of functions with values in partially ordered spaces
Medidas y probabilidades en estructuras ordenadas.
This paper is concerned with lattice-group valued measures for which the sygma-additivity is defined by means of the order convergence properties. In the first section we treat the analogues for such order-measures with values in a Dedekind complete lattice-group of the Jordan, Lebesgue and Yosida-Hewitt descompositions. The second section deals with the construction of an integral for functions with respect to an order-measure, both taking their values in a Dedekind sygma-complete lattice-ring....
Mesures -adiques à densité
Mesures vectorielles dans les espaces réticulés
On compact group-valued measures
On consequences of the Banach-Kuratowski theorem for Stone algebra valued measures
On convergence of integrals in o-minimal structures on archimedean real closed fields
We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.
On lifting quasi-Radon measures.
On locally solid topological lattice groups
Let be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If has the (iii)-property, then its completion is an order-complete locally solid lattice group. (2) If is order-complete and has the Fatou property, then the order intervals of are -complete. (3) If has the Fatou property, then is order-dense in and has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...
On measures and integrals with values in ordered groups
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 mappings generating vector -measures
On the extension of -poset valued measures
A variant of Alexandrov theorem is proved stating that a compact, subadditive -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.