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Liapounoff’s vector measure theorem in Banach spaces and applications to general equilibrium theory

Author

Listed:
  • Michael Greinecker

    (Universität Innsbruck)

  • Konrad Podczeck

    (Universität Wien)

Abstract

We present a result on convexity and weak compactness of the range of a vector measure with values in a Banach space, based on the Maharam classification of measure spaces. Our result extends a recent result of Khan and Sagara (Illinois J. Math. 2013). We apply our result to integration of Banach space valued correspondences and to the core-Walras equivalence problem in coalitional exchange economies with an infinite-dimensional commodity space.

Suggested Citation

  • Michael Greinecker & Konrad Podczeck, 2013. "Liapounoff’s vector measure theorem in Banach spaces and applications to general equilibrium theory," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 157-173, November.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0018-0
    DOI: 10.1007/s40505-013-0018-0
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    References listed on IDEAS

    as
    1. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-580, May.
    2. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
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    Citations

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    Cited by:

    1. Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
    2. Bhowmik, Anuj & Centrone, Francesca & Martellotti, Anna, 2019. "Coalitional extreme desirability in finitely additive economies with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 83-93.
    3. Niccolò Urbinati, 2020. "Walrasian objection mechanism and Mas Colell's bargaining set in economies with many commodities," Working Papers 07, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    4. 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.
    5. M. Ali Khan & Nobusumi Sagara, 2021. "Fuzzy Core Equivalence in Large Economies: A Role for the Infinite-Dimensional Lyapunov Theorem," Papers 2112.15539, arXiv.org.
    6. Urbinati, Niccolò, 2018. "A convexity result for the range of vector measures with applications to large economies," MPRA Paper 87185, University Library of Munich, Germany.
    7. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.

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    More about this item

    Keywords

    Liapounoff’s theorem; Vector measures; Correspondences; Blocking power of small coalitions; Core-Walras equivalence; Coalitional economies;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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