On Vector Measures in Cartesian Products

Miloslav Duchoň

A simple proof of the Borel extension theorem and weak compactness of operators

Ivan Dobrakov, Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let $T$ be a locally compact Hausdorff space and let $C_{0} (T)$ be the Banach space of all complex valued continuous functions vanishing at infinity in $T$ , provided with the supremum norm. Let $X$ be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of $X$ -valued $σ$ -additive Baire measures on $T$ is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear...

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