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.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 5 (1995)
Issue (Month): 3 (May)
Contact details of provider:
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985.
Cowles Foundation Discussion Papers
756R, Cowles Foundation for Research in Economics, Yale University.
- Aliprantis, Charalambos D. & Brown, Donald J., 1983.
"Equilibria in markets with a Riesz space of commodities,"
Journal of Mathematical Economics,
Elsevier, vol. 11(2), pages 189-207, April.
- Aliprantis, Charalambos D. & Brown, D. J., 1982. "Equilibrium in Markets with a Riesz Space of Commodities," Working Papers 427, California Institute of Technology, Division of the Humanities and Social Sciences.
- Darrell Duffie & William Zame, 1988.
"The Consumption-Based Capital Asset Pricing Model,"
88-10, University of Copenhagen. Department of Economics.
- Richard, Scott F. & Zame, William R., 1986. "Proper preferences and quasi-concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 231-247, June.
- Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
- Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
- Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
- Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
- Cherif, I. & Deghdak, M. & Florenzano, M., 1992.
"Existence of Equilibria in the Overlapping Generations Model; the Nontransitive Case,"
Papiers d'Economie MathÃÂ©matique et Applications
92-19, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Cherif, Imed & Deghdak, Messaoud & Florenzano, Monique, 1994. "Existence of Equilibria in the Overlapping Generations Model: The Nontransitive Case," Economic Theory, Springer, vol. 4(2), pages 217-35, March.
- Florenzano Monique & Cherif, Imed & Deghdak M, 1992. "Existence of equilibria in the overlapping generations model. the nontransitive case," CEPREMAP Working Papers (Couverture Orange) 9205, CEPREMAP.
- 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.
- Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-53, September.
- Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
- Araujo A. & Monteiro P. K., 1994. "The General Existence of Extended Price Equilibria with Infinitely Many Commodities," Journal of Economic Theory, Elsevier, vol. 63(2), pages 408-416, August.
- Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
- Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-77, October.
- Chichilnisky, Graciela & Kalman, P. J., 1979. "Application of functional analysis to models of efficient allocation of economic resources," MPRA Paper 8004, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.