Displaying similar documents to “On compact measures”

Conical measures and vector measures

Igor Kluvánek (1977)

Annales de l'institut Fourier

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Every conical measure on a weak complete space E is represented as integration with respect to a σ -additive measure on the cylindrical σ -algebra in E . The connection between conical measures on E and E -valued measures gives then some sufficient conditions for the representing measure to be finite.

Conical measures and properties of a vector measure determined by its range

L. Rodríguez-Piazza, M. Romero-Moreno (1997)

Studia Mathematica

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We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...