Economic Theory

, Volume 45, Issue 1–2, pp 1–22 | Cite as

On existence of rich Fubini extensions

  • Konrad PodczeckEmail author


This note presents new results on existence of rich Fubini extensions. The notion of a rich Fubini extension was recently introduced by Sun (J Econ Theory 126:31–69, 2006) and shown by him to provide the proper framework to obtain an exact law of large numbers for a continuum of random variables. In contrast to the existence results for rich Fubini extensions established by Sun, the arguments in this note do not use constructions from nonstandard analysis.


Fubini extension Exact law of large numbers Independence Risk 

JEL Classification

C00 C02 C60 


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  1. Alós-Ferrer C.: Individual Randomness in Economic Models with a Continuum of Agents. Working Paper, University of Vienna (2002)Google Scholar
  2. Anderson R.M.: Nonstandard analysis with applications to economics. In: Hildenbrand, W., Sonnenschein, H. (eds) Handbook of Mathematical Economics, Chap. 39, vol. IV, pp. 2145–2208. North-Holland, Amsterdam (1991)Google Scholar
  3. Aumann R.J.: Markets with a continuum of traders. Econometrica 32, 39–50 (1964)CrossRefGoogle Scholar
  4. Ciesielski K.: Set Theory for the Working Mathematician. London Mathematical Society Student Texts, vol. 39. Cambridge University Press, Cambridge (1997)Google Scholar
  5. Diamond D.W., Dybvig P.H.: Bank runs, deposit insurance and liquidity. J Polit Econ 91, 401–419 (1983)CrossRefGoogle Scholar
  6. Doob J.L.: Stochastic processes depending on a continuous parameter. Trans Am Math Soc 42, 107–140 (1937)Google Scholar
  7. Feldman M., Gilles C.: An expository note on individual risk without aggregate uncertainty. J Econ Theory 35, 26–32 (1985)CrossRefGoogle Scholar
  8. Fremlin D.H.: Measure Theory, vol. 3, Measure Algebras. Torres Fremlin, Colchester (2002)Google Scholar
  9. Fremlin D.H.: Measure Theory, vol. 4, Topological Measure Spaces. Torres Fremlin, Colchester (2003)Google Scholar
  10. Fremlin D.H.: Measure Theory, vol. 5, Set-Theoretic Measure Theory. Torres Fremlin, Colchester (2008)Google Scholar
  11. Green E.J.: Individual-Level Randomness in a Nonatomic Population. Working Paper, University of Minnesota (1994)Google Scholar
  12. Judd K.L.: The law of large numbers with a continuum of IID random variables. J Econ Theory 35, 19–25 (1985)CrossRefGoogle Scholar
  13. Keisler H.J., Sun Y.N.: Loeb measures and Borel algebras. In: Berger, U., Osswald, H., Schuster, P. (eds) Reuniting the Antipodes—Constructive and Nonstandard Views of the Continuum, pp. 111–118. Kluwer, Dordrecht (2001)Google Scholar
  14. Lucas R.E.: Equilibrium in a pure currency economy. Econ Inq 18, 203–220 (1980)CrossRefGoogle Scholar
  15. Podczeck K.: On purification of measure-valued maps. Econ Theory 38, 399–418 (2009)CrossRefGoogle Scholar
  16. Prescott E.C., Townsend R.M.: Pareto optima and competitive equilibria with adverse selection and moral hazard. Econometrica 52, 21–45 (1984)CrossRefGoogle Scholar
  17. Sun Y.N.: A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN. J Math Econ 29, 419–503 (1998)CrossRefGoogle Scholar
  18. Sun Y.N.: The exact law of large numbers via Fubini extension and characterization of insurable risks. J Econ Theory 126, 31–69 (2006)CrossRefGoogle Scholar
  19. Sun Y.N., Yannelis N.C.: Ex ante efficiency implies incentive compatibility. Econ Theory 36, 35–55 (2008)CrossRefGoogle Scholar
  20. Sun Y.N., Zhang Y.: Individual risk and Lebesgue extension without aggregate uncertainty. J Econ Theory 144, 432–443 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für WirtschaftswissenschaftenUniversität WienWienAustria

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