Displaying similar documents to “On Dieudonné's Boundedness Theorem”

Effect algebras and extensions of measures

Anna Avallone, Anna De Simone, Paolo Vitolo (2006)

Bollettino dell'Unione Matematica Italiana

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We investigate the existence of a Caratheodory type extension for modular measures defined on lattice-ordered effect algebras.

A Dieudonné theorem for lattice group-valued measures

Giuseppina Barbieri (2019)

Kybernetika

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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.

Modular atomic effect algebras and the existence of subadditive states

Zdena Riečanová (2004)

Kybernetika

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Lattice effect algebras generalize orthomodular lattices and M V -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.

An extension theorem for modular measures on effect algebras

Giuseppina Barbieri (2009)

Czechoslovak Mathematical Journal

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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.