IDEAS home Printed from https://ideas.repec.org/p/kan/wpaper/200503.html
   My bibliography  Save this paper

Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.ku.edu/~bgju/2005Papers/200503.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    2. 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.
    3. 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.
    4. repec:dau:papers:123456789/6273 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Bernard Cornet & Jean-Philippe Medecin, 2000. "Existence of General Equilibrium for Spatial Economies," Econometric Society World Congress 2000 Contributed Papers 1107, Econometric Society.
    8. 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.
    9. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    10. SCHMEIDLER, David, 1970. "Fatou's lemma in several dimensions," LIDAM Reprints CORE 46, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. 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.
    12. 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.
    13. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bernard Cornet & V. Filipe Martins-Da-Rocha, 2021. "Fatou's Lemma for Unbounded Gelfand Integrable Mappings," Post-Print hal-03506933, HAL.
    2. Martins-da-Rocha, Victor Filipe & Angeloni, Laura, 2008. "Large economies with differential information but without free disposal," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 671, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Angeloni, Laura & Martins-da-Rocha, Victor Filipe, 2007. "Contract enforcement and incentive compatibility in large economies with differential information: the role of exact feasibility," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 647, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    4. 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).
    5. Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
    6. repec:dau:papers:123456789/6273 is not listed on IDEAS
    7. repec:dau:papers:123456789/2344 is not listed on IDEAS
    8. Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 397-421, August.
    9. Laura Angeloni & V. Martins-da-Rocha, 2009. "Large economies with differential information and without free disposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 263-286, February.
    10. 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.
    11. Courtney LaFountain, 2008. "Core equivalence for residential land use models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 459-481, December.
    12. Suzuki, Takashi, 2013. "Core and competitive equilibria of a coalitional exchange economy with infinite time horizon," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 234-244.
    13. Hara, C., 2004. "Existence of Equilibria and Core Convergence in Economies with Bads," Cambridge Working Papers in Economics 0413, Faculty of Economics, University of Cambridge.
    14. Filipe Martins-da-Rocha, V., 2003. "Equilibria in large economies with a separable Banach commodity space and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 863-889, November.
    15. Jang, Hyo Seok & Lee, Sangjik, 2020. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 57-64.
    16. Ichiishi, Tatsuro, 1985. "Management versus ownership, II," European Economic Review, Elsevier, vol. 27(2), pages 115-138, March.
    17. Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    18. Jiuqiang Liu & Huihui Zhang, 2016. "Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1095-1109, November.
    19. Yamazaki, Akira & 山崎, 昭, 2001. "On a Problem of Proving the Existence of an Equilibrium in a Large Economy without Free Disposal: A problem of a purely finitely additive measure arising from the Fatou's lemma in several dimensions," Discussion Papers 2000-10, Graduate School of Economics, Hitotsubashi University.
    20. 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.
    21. Martin Shubik & Myrna Holtz Wooders, 1982. "Approximate Cores of a General Class of Economies: Part II. Set-Up Costs and Firm Formation in Coalition Production Economies," Cowles Foundation Discussion Papers 619, Cowles Foundation for Research in Economics, Yale University.
    22. Hyo Seok Jang & Sangjik Lee, 2019. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Papers 1904.07444, arXiv.org, revised Feb 2020.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:200503. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Zongwu Cai (email available below). General contact details of provider: https://edirc.repec.org/data/deuksus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.