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.
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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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Fernández, A., Mayoral, F., Naranjo, F. et al. Ordered representations of spaces of integrable functions. Positivity 13, 129–143 (2009). https://doi.org/10.1007/s11117-008-2211-1
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DOI: https://doi.org/10.1007/s11117-008-2211-1