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On extension of vector polymeasures. (English) Zbl 0688.28005

This is a continuation of Part VIII of the author’s series: “On integration in Banach spaces” [same journal 37(112), 487-506 (1987; Zbl 0688.28002)], where the concept of polymeasure was studied. Here the problem of extending vector polymeasures from a Cartesian product of rings to the Cartesian product of generated \(\sigma\)-rings is considered. The result is more definite in the case of uniform polymeasures, where Kluvánek’s theorem on extension of vector measures is used. The lack of the knowledge of the existence of control polymeasures prevents the dropping of uniformness condition.
Reviewer: Gr.Arsene

MSC:

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

Citations:

Zbl 0688.28002
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References:

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