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• W2023573653 abstract "Let ν be a vector measure with values in a Banach space Z. The integration map $$I_nu: L^1(nu)to Z$$ , given by $$fmapsto int f,dnu$$ for f ∈ L 1(ν), always has a formal extension to its bidual operator $$I_nu^{**}: L^1(nu)^{**}to Z^{**}$$ . So, we may consider the “integral” of any element f ** of L 1(ν)** as I ** (f **). Our aim is to identify when these integrals lie in more tractable subspaces Y of Z **. For Z a Banach function space X, we consider this question when Y is any one of the subspaces of X ** given by the corresponding identifications of X, X′′ (the Köthe bidual of X) and X′* (the topological dual of the Köthe dual of X). Also, we consider certain kernel operators T and study the extended operator I ** for the particular vector measure ν defined by ν(A) := T(χ A )." @default.
• W2023573653 created "2016-06-24" @default.
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• W2023573653 date "2008-04-05" @default.
• W2023573653 modified "2023-10-05" @default.
• W2023573653 title "Vector measures: where are their integrals?" @default.
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• W2023573653 doi "https://doi.org/10.1007/s11117-008-2191-1" @default.
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