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BV as a dual space

Fabio Maccheroni and William H. Ruckle

ICER Working Papers - Applied Mathematics Series from ICER - International Centre for Economic Research

Abstract: Let C be a field of subsets of a set I. It is well known that the space FA of all the finitely additive games of bounded variation on C is the norm dual of the space of all simple functions on C. In this paper we prove that the space BV of all the games of bounded variation on C is the norm dual of the space of all simple games on C. This result is equivalent to the compactness of the unit ball in BV with respect to the vague topology.

Keywords: Set functions; duality; compactness; coalitional games (search for similar items in EconPapers)
Pages: 10 pages
Date: 2001-10
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