Displaying similar documents to “Lattice-valued Borel measures. III.”

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 ) → E a positive linear map. First we give a new proof that μ extends to a unique, finitely additive measure μ ℱ → 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,...

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...

Decomposition of ℓ -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

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We deal with decomposition theorems for modular measures μ : L → G defined on a D-lattice with values in a Dedekind complete ℓ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete ℓ -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition...