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...
Partially additive states on orthomodular posets
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result may also...
Riesz-Presentation of Additive and -Additive Set-Valued Measures.
Some new results about Brooks-Jewett and Dieudonné-type theorems in -groups
In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for -group-valued measures.
Spaces of observables
The Additive Exhaustive Functions On M-Lattice
The additive exhaustive functions on M-lattice.
The Henstock-Kurzweil approach to Young integrals with integrators in
In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral exists if , and . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
The Kurzweil construction of an integral in ordered spaces
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space with respect to an ordered group valued measure are proved in this paper.
The monotone limit convergence theorem for elementary functions with values in a vector lattice
Vector Lattice Measures on Locally Compact Spaces.
Квазирадоновы меры.