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Mackey compactness in B(S)

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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 t(B(S), rca(S)). We also provide a short presentation of an economic application for an intertemporal allocation of resources

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  • Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf, 2021. "Mackey compactness in B(S)," Documents de travail du Centre d'Economie de la Sorbonne 21030, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:21030
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    1. 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.
    2. 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.
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