Ordered representations of spaces of integrable functions |
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| Authors: | Antonio Fernández Fernando Mayoral Francisco Naranjo Enrique A Sánchez–Pérez |
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| Institution: | (1) Dpto. Matemática Aplicada II, Escuela Técnica Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain;(2) Instituto Universitario de Matemática Pura y Aplicada (I.U.M.P.A.), Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain |
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| Abstract: | Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L1(n) = L1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation
of the space L1(m) associated to downward directed subsets of the set of all the representations.
This research has been partially supported by La Junta de Andalucía. The support of D.G.I. under project MTM2006–11690–C02
(M.E.C. Spain) and FEDER is gratefully acknowledged. |
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| Keywords: | Banach function space Vector measure Representation |
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