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The One-way Fubini Property and Conditional Independence : An Equivalence Result

Author

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  • Hammond, Peter J.

    (Department of Economics, University of Warwick)

  • Sun, Yeneng

    (Department of Mathematics, National University of Singapore)

Abstract

A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product sigma-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in our 2006 paper (“Joint measurability and the one-way Fubini property for a continuum of independent random variables”, Proceedings of the American Mathematical Society, 134: 737–747) to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a countably generated sigma-algebra given which the random variables are essentially pairwise conditionally independent, while their joint conditional distribution also satisfies a suitable joint measurability condition. Applications include new characterizations of essential pairwise independence and essential pairwise exchangeability through regular conditional distributions with respect to the usual product sigma-algebra in the framework of a one-way Fubini extension.

Suggested Citation

  • Hammond, Peter J. & Sun, Yeneng, 2016. "The One-way Fubini Property and Conditional Independence : An Equivalence Result," CRETA Online Discussion Paper Series 22, Centre for Research in Economic Theory and its Applications CRETA.
    • Handle: RePEc:wrk:wcreta:22
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/22_-_the_one-way_fubini_property_and_conditional_independence.pdf
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    References listed on IDEAS

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    1. 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.
    2. Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
    3. J. W. Milnor & L. S. Shapley, 1978. "Values of Large Games II: Oceanic Games," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 290-307, November.
    4. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    5. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
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    Cited by:

    1. Peter J. Hammond & Lei Qiao & Yeneng Sun, 2021. "Monte Carlo sampling processes and incentive compatible allocations in large economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1161-1187, April.

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