Product of vector measures on topological spaces

Surjit Singh Khurana

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

Embedding $c_{0}$ in $bvca (Σ, X)$

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

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If $(Ω, Σ)$ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $Σ$ and $X$ in order to guarantee that $b v c a (Σ, X)$ , the Banach space of all $X$ -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_{0}$ if and only if $X$ does.

On Pettis integrability

Juan Carlos Ferrando (2003)

Czechoslovak Mathematical Journal

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Assuming that $(Ω, Σ, μ)$ is a complete probability space and $X$ a Banach space, in this paper we investigate the problem of the $X$ -inheritance of certain copies of $c_{0}$ or $ℓ_{\infty}$ in the linear space of all [classes of] $X$ -valued $μ$ -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.

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...

Order convergence of vector measures on topological spaces

Surjit Singh Khurana (2008)

Mathematica Bohemica

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Let $X$ be a completely regular Hausdorff space, $E$ a boundedly complete vector lattice, $C_{b} (X)$ the space of all, bounded, real-valued continuous functions on $X$ , $ℱ$ the algebra generated by the zero-sets of $X$ , and $μ C_{b} (X) \to E$ a positive linear map. First we give a new proof that $μ$ extends to a unique, finitely additive measure $μ ℱ \to E^{+}$ such that $ν$ is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of $E^{+}$ -valued finitely additive measures on $ℱ$ are proved,...

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

Embedding c 0 in bvca ( Σ , X )

On Pettis integrability

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

Order convergence of vector measures on topological spaces

Embedding $c_{0}$ in $bvca (Σ, X)$