A Representation Theorem for Riesz Spaces and Its Applications to Economics
AbstractWe 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.
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Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 5 (1995)
Issue (Month): 3 (May)
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Web page: http://link.springer.de/link/service/journals/00199/index.htm
Other versions of this item:
- William R. Zame & Y.A. Abramovich & C.D. Aliprantis, 1994. "A Representation Theorem for Riesz Spaces and its Applications to Economics," UCLA Economics Working Papers 725, UCLA Department of Economics.
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