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Individual Level Randomness in a Nonatomic Population

  • Edward J. Green

    (University of Minnesota and Federal Reserve Bank of Minneapolis)

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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File URL: http://128.118.178.162/eps/ge/papers/9402/9402001.pdf
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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
Date of revision:
Handle: RePEc:wpa:wuwpge:9402001
Note: plain TeX, title 15 pages.
Contact details of provider: Web page: http://128.118.178.162

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  1. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  2. Harald Uhlig, 2010. "A Law of Large Numbers for Large Economies," Levine's Working Paper Archive 2070, David K. Levine.
  3. 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.
  4. 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.
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