On the average of inner and outer measures
D. Fremlin (1991)
Fundamenta Mathematicae
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D. Fremlin (1991)
Fundamenta Mathematicae
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Yoshihiro Kubokawa (1995)
Czechoslovak Mathematical Journal
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Kazimierz Musiał (1980)
Fundamenta Mathematicae
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Monika Remy (1988)
Manuscripta mathematica
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Schaerf, H.M. (1949)
Portugaliae mathematica
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Jan Mycielski (1967)
Fundamenta Mathematicae
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B. Jessen (1948)
Colloquium Mathematicae
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Kharazishvili, A.B. (1997)
Journal of Applied Analysis
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A. Ülger (2007)
Studia Mathematica
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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)
Extracta Mathematicae
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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...