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In this paper we study the validity of several convergence theorems for measures defined on an effect algebra and taking values in a Hausdorff commutative topological group. We establish the Brooks-Jewett theorem and the Nikodym convergence theorem, giving as a corollary a result, due to Aarnes, about the convergence of a sequence of normal linear functionals on a von Neumann algebra. We prove two new convergence theorems concerning completely additive and r-smooth measures, and we obtain also a convergence theorem for regular measures.

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On the Alexandroff decomposition theorem

Avallone

Barbieri

Vitolo

2008

Mathematica Slovaca

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Cited by 4 publications

References 7 publications

On topological MV-algebras and topological ℓ-groups

On topological MV-algebras and topological ℓ-groups

Convergence theorems for topological group valued measures on effect algebras

On the Alexandroff decomposition theorem

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