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Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings

Author

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  • Bernard Cornet

    (Department of Economics, The University of Kansas)

  • V. F. Martins-Da-Rocha

Abstract

It is shown that, in the framework of Gelfand integrable mappings, the Fatou-type lemma for integrably bounded mappings, due to Cornet?Medecin [14] and the Fatou-type lemma for uniformly integrable mappings due to Balder [9], can be generalized to mean norm bounded integrable mappings

Suggested Citation

  • Bernard Cornet & V. F. Martins-Da-Rocha, 2005. "Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200503, University of Kansas, Department of Economics, revised Feb 2005.
    • Handle: RePEc:kan:wpaper:200503
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    File URL: http://www.ku.edu/~bgju/2005Papers/200503.pdf
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    References listed on IDEAS

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    1. Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 385-426.
    2. Bernard Cornet & Jean-Philippe Medecin, 2000. "Existence of General Equilibrium for Spatial Economies," Econometric Society World Congress 2000 Contributed Papers 1107, Econometric Society.
    3. Aloisio Araujo & V. Martins-da-Rocha & Paulo Monteiro, 2004. "Equilibria in reflexive Banach lattices with a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 469-492, October.
    4. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    5. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    6. SCHMEIDLER, David, 1970. "Fatou's lemma in several dimensions," LIDAM Reprints CORE 46, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Ostroy, Joseph M & Zame, William R, 1994. "Nonatomic Economies and the Boundaries of Perfect Competition," Econometrica, Econometric Society, vol. 62(3), pages 593-633, May.
    8. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    9. V. Martins-da-Rocha, 2004. "Equilibria in large economies with differentiated commodities and non-ordered preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 529-552, March.
    10. Erik J. Balder & Christian Hess, 1995. "Fatou's Lemma for Multifunctions with Unbounded Values," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 175-188, February.
    11. HILDENBRAND, Werner, 1970. "Existence of equilibria for economies with production and a measure space of consumers," LIDAM Reprints CORE 79, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. repec:dau:papers:123456789/6273 is not listed on IDEAS
    13. Cornet, Bernard & Topuzu, Mihaela & Yildiz, Aysegul, 2003. "Equilibrium theory with a measure space of possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 175-196, June.
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    Cited by:

    1. Page, Frank, 2015. "A fixed point theorem for measurable-selection-valued correspondences arising in game theory," LSE Research Online Documents on Economics 65101, London School of Economics and Political Science, LSE Library.
    2. Monteiro, P. K. & Araújo, Aloísio Pessoa de & Martins-da-Rocha, Victor Filipe, 2003. "Equilibria in security markets with a continuum of agents," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 513, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. repec:dau:papers:123456789/6273 is not listed on IDEAS

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