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Completeness of the \(L^ 1\)-space of closed vector measures. (English) Zbl 0668.46019

The notion of a closed vector measure m, due to I. Kluvànek, 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 \(L^ 1\)-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 \(L^ 1(m)\) for closed X-valued measures m are presentend without the requirement that X be sequentially complete.
Reviewer: W.J.Ricker

MSC:

46G10 Vector-valued measures and integration
28B05 Vector-valued set functions, measures and integrals
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References:

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