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Individual Level Randomness in a Nonatomic Population

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Author Info
Edward J. Green (University of Minnesota and Federal Reserve Bank of Minneapolis)

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Abstract

This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) samples are measurable functions from the index space, and (b) an exact analogue of the Glivenko-Cantelli theorem holds with respect to the measure on that space. That is, a sample possesses a.s. the same distribution as that of the random vectors from which it is drawn. Moreover, any subspace of the index space with positive measure inherits the same property. This homogeneity property is important for an application of the construction to mathematical economics.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 9402001.

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Length: 15 pages
Date of creation: 26 Feb 1994
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Handle: RePEc:wpa:wuwpge:9402001

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
D5 - Microeconomics - - General Equilibrium and Disequilibrium
D9 - Microeconomics - - Intertemporal Choice and Growth

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.:

  1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February. [Downloadable!] (restricted)
  2. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February. [Downloadable!] (restricted)
  3. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer, vol. 8(1), pages 41-50.
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Cited by:
(explanations, 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.)

  1. Darrell Duffie & Yeneng Sun, 2004. "The Exact Law of Large Numbers for Independent Random Matching," Levine's Bibliography 122247000000000328, UCLA Department of Economics. [Downloadable!]
  2. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany. [Downloadable!]
  3. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation, Yale University. [Downloadable!]
  4. Aidt, T.S. & Giovannoni,F., 2005. "Critical Decisions and Constitutional Rules," Cambridge Working Papers in Economics 0523, Faculty of Economics, University of Cambridge. [Downloadable!]
  5. Edward J. Green, 1991. "Eliciting traders' knowledge in "frictionless" asset market," Staff Report 144, Federal Reserve Bank of Minneapolis. [Downloadable!]
  6. Peter J. Hammond & Yeneng Sun, 2000. "Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables," Working Papers 00008, Stanford University, Department of Economics. [Downloadable!]
  7. Boylan, Richard T., 1990. "Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals," Working Papers 748, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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