Order convergence of vector measures on topological spaces

Surjit Singh Khurana

Displaying similar documents to “Order convergence of vector measures on topological spaces”

Positive vector measures with given marginals

Surjit Singh Khurana (2006)

Czechoslovak Mathematical Journal

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Suppose $E$ is an ordered locally convex space, $X_{1}$ and $X_{2}$ Hausdorff completely regular spaces and $Q$ a uniformly bounded, convex and closed subset of $M_{t}^{+} (X_{1} \times X_{2}, E)$ . For $i = 1, 2$ , let $μ_{i} \in M_{t}^{+} (X_{i}, E)$ . Then, under some topological and order conditions on $E$ , necessary and sufficient conditions are established for the existence of an element in $Q$ , having marginals $μ_{1}$ and $μ_{2}$ .

Lattice-valued Borel measures. III.

Surjit Singh Khurana (2008)

Archivum Mathematicum

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Let $X$ be a completely regular $T_{1}$ space, $E$ a boundedly complete vector lattice, $C (X)$ $(C_{b} (X))$ the space of all (all, bounded), real-valued continuous functions on $X$ . In order convergence, we consider $E$ -valued, order-bounded, $σ$ -additive, $τ$ -additive, and tight measures on X and prove some order-theoretic and topological properties of these measures. Also for an order-bounded, $E$ -valued (for some special $E$ ) linear map on $C (X)$ , a measure representation result is proved. In case $E_{n}^{*}$ separates...

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...

On vector measures

Corneliu Constantinescu (1975)

Annales de l'institut Fourier

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Let $ℳ$ be the Banach space of real measures on a $σ$ -ring $R$ , let $ℳ^{'}$ be its dual, let $E$ be a quasi-complete locally convex space, let $E^{'}$ be its dual, and let $μ$ be an $E$ -valued measure on $R$ . If is shown that for any $θ \in ℳ^{'}$ there exists an element $\int θ d μ$ of $E$ such that $⟨ x^{'} \circ μ, θ ⟩ = ⟨\int θ d μ, x^{'}⟩$ for any $x^{'} \in E^{'}$ and that the map $θ \to \int θ d μ : ℳ^{'} \to E$ is order continuous. It follows that the closed convex hull of $μ (R)$ is weakly compact.