Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces |
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Authors: | JM Calabuig P Gregori |
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Institution: | a Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, València 46022, Spain b Departament de Matemàtiques, Universitat Jaume I de Castelló, Campus Riu Sec, E-12071 Castelló de la Plana, Spain |
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Abstract: | Let m, n be a couple of vector measures with values on a Banach space. We develop a separation argument which provides a characterization of when the Radon-Nikodým derivative of n with respect to m—in the sense of the Bartle-Dunford-Schwartz integral—exists and belongs to a particular sublattice Z(μ) of the space of integrable functions L1(m). We show that this theorem is in fact a particular feature of our separation argument, which can be applied to prove other results in both the vector measure and the function space settings. |
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Keywords: | Vector measures Kö the function spaces Radon-Nikodý m |
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