On Dieudonné's Boundedness Theorem

Giuseppina Barbieri

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.

Separating points of measures on effect algebras

Anna Avallone (2007)

Mathematica Slovaca

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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.

Lyapunov measures on effect algebras

Anna Avallone, Giuseppina Barbieri (2003)

Commentationes Mathematicae Universitatis Carolinae

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We prove a Lyapunov type theorem for modular measures on lattice ordered effect algebras.

Two extension theorems. Modular functions on complemented lattices

Hans Weber (2002)

Czechoslovak Mathematical Journal

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We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions...