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A generalization of Fubini’s theorem for Banach algebra-valued measures. (English) Zbl 0556.28010

The well known Fubini’s theorem for Bochner integrals is generalized when the countably additive vector measures \(\mu_ 1\) and \(\mu_ 2\) of bounded variation on the \(\sigma\)-rings \(S_ 1\) and \(S_ 2\) and the vector valued function f(.,.) assume values in a Banach algebra X. No topological hypothesis such as local-compactness, regularity etc. is needed in the proof. Under such topological conditions the result is already known. N. Dinculeanu, ’Integration on locally compact spaces’ (1974; Zbl 0284.28003).

MSC:

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

Citations:

Zbl 0284.28003
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