A Representation Theorem for Riesz Spaces and Its Applications to EconomicsY A Abramovich, C D Aliprantis and William R. Zame Economic Theory, 1995, vol. 5, issue 3, pages 527-35 Abstract: We show that a Dedekind complete Riesz space which contains a weak unit e and admits a strictly positive order continuous linear functional can be represented as a subspace of the space L(subscript "1") of integrable functions on a probability measure space in such a way that the order ideal generated by e is carried onto L(subscript "infinity"). As a consequence, we obtain a characterization of abstract M-spaces that are isomorphic to concrete L(subscript "infinity")-spaces. Although these results are implicit in the literature on representation of Riesz spaces, they are not available in this form. This research is motivated by, and has applications in, general equilibrium theory in infinite dimensional spaces. There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Ordering information: This journal article can be ordered from Access Statistics for this article Economic Theory is edited by C.D. Aliprantis More articles in Economic Theory from Springer |
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