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Mackey compactness in B(S)

Author

Listed:
  • Aloisio Araujo

    (IMPA - Instituto Nacional de Matemática Pura e Aplicada)

  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

Let S be a set equipped with the discrete topology and B(S) be the normed space of bounded real mappings on S, endowed with the sup-norm. In this paper, we first prove that B(S) is the nom dual of the space rca(S) of all regular and bounded Borel measure on S. Then we show that the closed unit ball of B(S) is compact in the Mackey topology τ (B(S), rca(S)). We also provide a short presentation of an economic application for an intertemporal allocation of resources.

Suggested Citation

  • Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf, 2021. "Mackey compactness in B(S)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03461538, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03461538
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03461538
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    References listed on IDEAS

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    1. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2017. "Optimal sharing with an infinite number of commodities in the presence of optimistic and pessimistic agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 131-157, January.
    2. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Nunez-Sanz, Carmelo & Rui Pascoa, Mario, 2000. "Blocking Efficacy of Small Coalitions in Myopic Economies," Journal of Economic Theory, Elsevier, vol. 93(1), pages 72-86, July.
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