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.
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Length: 10 pages Date of creation: Oct 2001 Date of revision: Handle: RePEc:icr:wpmath:29-2001
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001.
"A Subjective Spin on Roulette Wheels,"
Working Papers
1127, California Institute of Technology, Division of the Humanities and Social Sciences.
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