A representation theorem for Riesz spaces and its applications to economics View Full Text


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Article Info

DATE

1995-10

AUTHORS

Y. A. Abramovich, C. D. Aliprantis, W. R. Zame

ABSTRACT

We show that a Dedekind complete Riesz space which contains a weak unite and admits a strictly positive order continuous linear functional can be represented as a subspace of the spaceL1 of integrable functions on a probability measure space in such a way that the order ideal generated bye is carried ontoLt8. As a consequence, we obtain a characterization of abstractM-spaces that are isomorphic to concreteL∞-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. More... »

PAGES

527-535

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01212332

DOI

http://dx.doi.org/10.1007/bf01212332

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027813178


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