An extension theorem for modular measures on effect algebras

Barbieri, Giuseppina

doi:10.1007/s10587-009-0042-2

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…In [16,17], measures on effect algebras with values on a commutative topological group are considered. Later, in [18][19][20][21], the authors study vector-valued measures on effect algebras, that is, with values on real or complex Hausdorff locally convex topological vector spaces. A few years later, measures on effect algebras with values on a real or complex normed space were considered in [22,23].…”

Section: Introductionmentioning

confidence: 99%

The Range of a Module Measure Defined on an Effect Algebra

García-Pacheco

2022

Symmetry

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Effect algebras are the main object of study in quantum mechanics. Module measures are those measures defined on an effect algebra with values on a topological module. Let R be a topological ring and M a topological R-module. Let L be an effect algebra. The range of a module measure μ:L→M is studied. Among other results, we prove that if L is an sRDP σ-effect algebra with a natural basis and μ:L→R is a countably additive measure, then μ has bounded variation.

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Section: Introductionmentioning

confidence: 99%

The Range of a Module Measure Defined on an Effect Algebra

García-Pacheco

2022

Symmetry

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Topological Ordered Rings and Measures

García-Pacheco,

Moreno-Frías,

Murillo-Arcila

2023

Results Math

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Given a ring endowed with a ring order, we provide sufficient conditions for the order topology induced by the ring order to become a ring topology (analogous results for module orders are consequently derived). Finally, the notions of Radon and regular measures are transported to the scope of module-valued measures through module orders. Classical characterizations of these measures are obtained as well as the hereditariness of regularity for conditional ring-valued measures.

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Convergence Theorems for Lattice Group-Valued Measures

Boccuto

Dimitriou

2015

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An extension theorem for modular measures on effect algebras

Cited by 3 publications

References 24 publications

The Range of a Module Measure Defined on an Effect Algebra

The Range of a Module Measure Defined on an Effect Algebra

Topological Ordered Rings and Measures

Convergence Theorems for Lattice Group-Valued Measures

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