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

Khurana, Surjit Singh

Commentat. Math. Univ. Carol. 49, No. 3, 421-435 (2008).

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.

Reviewer: Bohumír Opic (Praha)

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

Keywords:

injective tensor product; product of measures; tight measures; \(\tau \)-smooth measures; separable measures; Fubini theorem