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An ordered suprabarrelled space

Part of: Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  09 April 2009

J. C. Ferrando  and
M. López-Pellicer
M. López-Pellicer
Affiliation:
Departmento de Matemática Aplicada (ETSIA) Universidad Politécnica de ValenciaApartado 22012 46071-ValenciaSpain
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Abstract

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A locally convex space E is said to be ordered suprabarrelled if given any increasing sequence of subspaces of E covering E there is one of them which is suprabarrelled. In this paper we show that the space m0(X, Σ), where X is any set and Σ is a σ-algebra on X, is ordered suprabarrelled, given an affirmative answer to a previously raised question. We also include two applications of this result to the theory of vector measures.

Keywords

barrelled spacesuprabarrelled space.

MSC classification

Secondary: 28C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 106 - 117
Copyright
Copyright © Australian Mathematical Society 1991

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