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Product of vector measures on topological spaces. (English) Zbl 1212.46064

Let \(X_i\) and \(E_i\) \((i=1,2)\) be completely regular Hausdorff spaces and quasi-complete locally convex spaces, respectively. Let \(E=E_i\mathrel {\breve {\otimes }}E_2\) be the completion of the injective tensor product of \(E_1\) and \(E_2\). Denote by \(\mathcal A_i\) \(\sigma \)-algebras of subsets of \(X_i\) and let \(\mu _i \: \mathcal A_i\to E_i\) \((i=1,2)\) be countably additive vector measures. The author establishes conditions that guarantee the existence of the \(E\)-valued product measure \(\mu _1\otimes \mu _2\) which has certain Fubini-type properties.

MSC:

46G10 Vector-valued measures and integration
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
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