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Product vector measures via Bartle integrals. (English) Zbl 0551.28009

The authors consider the product of two measures with values in locally convex topological vector spaces X, Y, with respect to a given bilinear map \(X\times Y\to Z\), where Z is also a locally convex topological vector space. They prove also the existence of an integral representation of the product measure, which generalizes Bartle’s *-integral. This has been proved for measures fulfilling boundedness and absolute continuity conditions with respect to a positive finite measure. There are given comprehensive examples of measures which fail to have the latter property.
Reviewer: P.Kruszynski

MSC:

28B05 Vector-valued set functions, measures and integrals
28A35 Measures and integrals in product spaces
46G10 Vector-valued measures and integration
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References:

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