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A Representation Theorem for Riesz Spaces and its Applications to Economics

Author

Listed:
  • William R. Zame

    (UCLA)

  • Y.A. Abramovich

    (IUPUI)

  • C.D. Aliprantis

    (IUPUI)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
  • Handle: RePEc:cla:uclawp:725
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    File URL: http://www.econ.ucla.edu/workingpapers/wp725.pdf
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    4. Jeffrey R. Brown, 2014. "Introduction," Tax Policy and the Economy, University of Chicago Press, vol. 28(1), pages 1-1.
    5. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
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    Cited by:

    1. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Hilbert A-Modules," Working Papers 544, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2016. "Orthogonal Decompositions in Hilbert A-Modules," Working Papers 577, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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