On the role of an intersection property in measure theory - I
Schaerf, H.M. (1949)
Portugaliae mathematica
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Schaerf, H.M. (1949)
Portugaliae mathematica
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Czesław Ryll-Nardzewski (1953)
Fundamenta Mathematicae
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Igor Kluvánek (1977)
Annales de l'institut Fourier
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Every conical measure on a weak complete space is represented as integration with respect to a -additive measure on the cylindrical -algebra in . The connection between conical measures on and -valued measures gives then some sufficient conditions for the representing measure to be finite.
Edward Marczewski, Czesław Ryll-Nardzewski (1953)
Fundamenta Mathematicae
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Wilbur, John (1973)
Portugaliae mathematica
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D. Fremlin (1991)
Fundamenta Mathematicae
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Schaerf, H.M. (1951)
Portugaliae mathematica
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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...
Maharam, Dorothy (1987)
Portugaliae mathematica
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