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Completeness of the L1-space of closed vector measures

Published online by Cambridge University Press:  20 January 2009

Werner J. Ricker
Werner J. Ricker
Affiliation:
Fachbereich Mathematik, Universität des Saarlandes, D-6600 Saarbrücken, Federal Republic of Germany
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Abstract

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The notion of a closed vector measure m, due to I. Kluv´;nek, is by now well established. Its importance stems from the fact that if the locally convex space X in which m assumes its values is sequentially complete, then m is closed if and only if its L1-space is complete for the topology of uniform convergence of indefinite integrals. However, there are important examples of X-valued measures where X is not sequentially complete. Sufficient conditions guaranteeing the completeness of L1(m) for closed X-valued measures m are presented without the requirement that X be sequentially complete.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 71 - 78
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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