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A Dieudonné theorem for lattice group-valued measures

Giuseppina Barbieri (2019)


A version of Dieudonné theorem is proved for lattice group-valued modular measures on lattice ordered effect algebras. In this way we generalize some results proved in the real-valued case.

Convergence theorems for measures with values in Riesz spaces

Domenico Candeloro (2002)


In some recent papers, results of uniform additivity have been obtained for convergent sequences of measures with values in l -groups. Here a survey of these results and some of their applications are presented, together with a convergence theorem involving Lebesgue decompositions.

Decomposition of group-valued measures on orthoalgebras

Paolo De Lucia, Pedro Morales (1998)

Fundamenta Mathematicae

We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the case where the measure is order bounded instead of being positive. This last result generalizes A. D. Aleksandrov's...

Decomposition of -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

We deal with decomposition theorems for modular measures μ : L G defined on a D-lattice with values in a Dedekind complete -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for -group-valued...

Dieudonné-type theorems for lattice group-valued k -triangular set functions

Antonio Boccuto, Xenofon Dimitriou (2019)


Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for k -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.

Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

Ideal convergence and divergence of nets in ( ) -groups

Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou (2012)

Czechoslovak Mathematical Journal

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 ( D ) -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...

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