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Individual Level Randomness in a Nonatomic Population

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  • Edward J. Green

    (University of Minnesota and Federal Reserve Bank of Minneapolis)

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.

Suggested Citation

  • Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:9402001
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    References listed on IDEAS

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    1. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
    2. 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.
    3. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    4. 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.
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    Cited by:

    1. Larson, Nathan, 2015. "Inertia in social learning from a summary statistic," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 596-626.
    2. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    3. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
    4. Toke Aidt & Francesco Giovannoni, 2011. "Critical decisions and constitutional rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(2), pages 219-268, July.
    5. Edward J. Green, 1991. "Eliciting traders' knowledge in "frictionless" asset market," Staff Report 144, Federal Reserve Bank of Minneapolis.
    6. Nick Netzer & Florian Scheuer, 2014. "A Game Theoretic Foundation Of Competitive Equilibria With Adverse Selection," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 399-422, May.
    7. Richard T. Boylan, 1997. "Laws of Large Numbers for Dynamical Systems with Random Matched Individuals," Levine's Working Paper Archive 845, David K. Levine.
    8. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," NBER Working Papers 8190, National Bureau of Economic Research, Inc.
    9. Bilbiie, Florin Ovidiu & Ragot, Xavier, 2017. "Optimal Monetary Policy and Liquidity with Heterogeneous Households," CEPR Discussion Papers 11814, C.E.P.R. Discussion Papers.
    10. François Grand & Xavier Ragot, 2016. "Incomplete markets and derivative assets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 517-545, August.
    11. 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.
    12. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, August.
    13. Huang, Ming, 2003. "Liquidity shocks and equilibrium liquidity premia," Journal of Economic Theory, Elsevier, vol. 109(1), pages 104-129, March.
    14. Duffie, Darrell & Sun, Yeneng, 2012. "The exact law of large numbers for independent random matching," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1105-1139.
    15. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    16. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers 9807, University of Vienna, Department of Economics.
    17. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2018. "Dynamic directed random matching," Journal of Economic Theory, Elsevier, vol. 174(C), pages 124-183.
    18. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    19. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
    20. Xavier Ragot & Florin O. Bilbiie, 2016. "Monetary Policy, Inflation, and Inequality: The Case for Helicopters," 2016 Meeting Papers 1663, Society for Economic Dynamics.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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