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Convergence theorems for topological group valued measures on effect algebras

Published online by Cambridge University Press:  17 April 2009

Francisco García Mazarío
Francisco García Mazarío
Affiliation:
Departamento de Matemática Aplicada (E. U. Informática), Universidad Politécnica de Madrid, 28031-Madrid, Spain, e-mail: [email protected]
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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 Nikodým 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 τ-smooth measures, and we obtain also a convergence theorem for regular measures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 213 - 231
Copyright
Copyright © Australian Mathematical Society 2001

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