Mackey compactness in B(S)

Aloisio Araujo (), Jean-Marc Bonnisseau and Alain Chateauneuf
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Aloisio Araujo: IMPA - Instituto Nacional de Matemática Pura e Aplicada

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

Keywords: Mackey compactness; bounded mappings; regular Borel measure; norm dual; Compacité au sens de Mackey; fonction bornée; mesure de Borel régulière; dual pour la topologie de la norme (search for similar items in EconPapers)
Date: 2021-03
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03461538v1
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Published in 2021

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Related works:
Working Paper: Mackey compactness in B(S) (2021)
Working Paper: Mackey compactness in B(S) (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03461538

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