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 L 1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1(n) = L 1(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 L 1(m) associated to downward directed subsets of the set of all the representations.
Positivity – Springer Journals
Published: Sep 1, 2008
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