On Dieudonné's Boundedness Theorem
We generalize the classical Dieudonné boundedness theorem for modular measures on lattice ordered effect algebras.
An extension theorem for modular measures on effect algebras
We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
Convergent regular measures on MV–algebras
We obtain for measures on MV-algebras the classical theorem of Dieudonné related to convergent sequences of regular maps.
A Dieudonné theorem for lattice group-valued measures
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.
Lyapunov measures on effect algebras
We prove a Lyapunov type theorem for modular measures on lattice ordered effect algebras.
Central Elements in Pseudo-D-Lattices and Hahn Decomposition Theorem
We prove a Hahn decomposition theorem for modular measures on pseudo-D-lattices. As a consequence, we obtain a Uhl type theorem and a Kadets type theorem concerning compactness and convexity of the closure of the range.
Control and separating points of modular functions
Decomposition of -group-valued measures
We deal with decomposition theorems for modular measures 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...
Misure su --semigruppi e su MV-algebre
Lineability and spaceability on vector-measure spaces
It is proved that if X is infinite-dimensional, then there exists an infinite-dimensional space of X-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that , the measures with non-σ-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl....
Addendum to "Lineability and spaceability of vector-measure spaces" (Studia Math. 219 (2013), 155-161)
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