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.
On the extension of measures
On the extension of subadditive measures in lattice ordered groups
A lattice ordered group valued subadditive measure is extended from an algebra of subsets of a set to a -algebra.
On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with...
On the Kurzweil integral for functions with values in ordered spaces. II.
On the lattice group valued measures
On the lattice group valued submeasures
On various notions of regularity in ordered spaces
On vector lattice-valued measures. I.
Order convergence of vector measures on topological spaces
Let be a completely regular Hausdorff space, a boundedly complete vector lattice, the space of all, bounded, real-valued continuous functions on , the algebra generated by the zero-sets of , and a positive linear map. First we give a new proof that extends to a unique, finitely additive measure such that is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of -valued finitely additive measures on are proved, which extend...