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BV as a dual space

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Author Info

  • Fabio Maccheroni

    ()

  • William H. Ruckle

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.

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File URL: http://www.icer.it/docs/wp2001/maccheroni29-01.pdf
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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 29-2001.

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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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Related research

Keywords: Set functions; duality; compactness; coalitional games;

References

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  1. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research.
  2. Adriana Castaldo & Massimo Marinacci, 2001. "Random correspndences as bundles of random variables," ICER Working Papers - Applied Mathematics Series 12-2001, ICER - International Centre for Economic Research.
  3. Marinacci, Massimo & Montrucchio, Luigi, 2003. "Subcalculus for set functions and cores of TU games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 1-25, February.
  4. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," POLIS Working Papers 5, Institute of Public Policy and Public Choice - POLIS.
  5. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  6. Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research.
  7. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
  8. Maitreesh Ghatak & Massimo Morelli & Tomas Sjostrom, 2002. "Credit Rationing, Wealth Inequality, and Allocation of Talent," Economics Working Papers 0026, Institute for Advanced Study, School of Social Science.
  9. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
  10. Fabio Maccheroni, 2004. "Yaari's dual theory without the completeness axiom," Economic Theory, Springer, vol. 23(3), pages 701-714, March.
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Citations

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Cited by:
  1. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Economics Papers from University Paris Dauphine 123456789/6223, Paris Dauphine University.
  2. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
  3. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.

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