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The range of an o-weakly compact mapping

Part of: Topological linear spaces and related structures Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  09 April 2009

P. G. Dodds
P. G. Dodds
Affiliation:
School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, S.A. 5042, Australia
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Abstract

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It is shown that a weakly compact convex set in a locally convex space is a zonoform if and only if it is the order continuous image of an order interval in a Dedekind complete Riesz space. While this result implies the Kluv´nek characterization of the range of a vector measure, the techniques of the present paper are purely order theoretic.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices 28B05: Vector-valued set functions, measures and integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 391 - 399
Copyright
Copyright © Australian Mathematical Society 1985

References

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