IDEAS home Printed from https://ideas.repec.org/p/wrk/wcreta/22.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/22_-_the_one-way_fubini_property_and_conditional_independence.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
    2. 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.
    3. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    4. 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.
    5. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Core, equilibria and incentives in large asymmetric information economies," Games and Economic Behavior, Elsevier, vol. 61(1), pages 131-155, October.
    6. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    7. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
    8. Sun, Xiang & Sun, Yeneng & Wu, Lei & Yannelis, Nicholas C., 2017. "Equilibria and incentives in private information economies," Journal of Economic Theory, Elsevier, vol. 169(C), pages 474-488.
    9. Scotchmer, Suzanne & Shannon, Chris, 2019. "Verifiability and group formation in markets," Journal of Economic Theory, Elsevier, vol. 183(C), pages 417-477.
    10. Yeneng Sun & Lei Wu & Nicholas C. Yannelis, 2011. "Existence, Incentive Compatibility and Efficiency of the Rational Expectations Equilibrium," Economics Discussion Paper Series 1108, Economics, The University of Manchester.
    11. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Perfect competition in asymmetric information economies: compatibility of efficiency and incentives," Journal of Economic Theory, Elsevier, vol. 134(1), pages 175-194, May.
    12. 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.
    13. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).
    14. Martin F. Hellwig, 2021. "Public-Good Provision with Macro Uncertainty about Preferences: Efficiency, Budget Balance, and Robustness," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2021_19, Max Planck Institute for Research on Collective Goods.
    15. Francesca Biagini & Andrea Mazzon & Thilo Meyer-Brandis & Katharina Oberpriller, 2022. "Liquidity based modeling of asset price bubbles via random matching," Papers 2210.13804, arXiv.org, revised Nov 2022.
    16. Yeneng Sun & Lei Wu & Nicholas C. Yannelis, 2013. "Incentive compatibility of rational expectations equilibrium in large economies: a counterexample," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-10, May.
    17. Alexander Aurell & René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Finite State Graphon Games with Applications to Epidemics," Dynamic Games and Applications, Springer, vol. 12(1), pages 49-81, March.
    18. Sun, Yeneng & Wu, Lei & Yannelis, Nicholas C., 2012. "Existence, incentive compatibility and efficiency of the rational expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 76(1), pages 329-339.
    19. Jonas Hedlund & Carlos Oyarzun, 2018. "Imitation in heterogeneous populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 937-973, June.
    20. Li, Fei & Song, Yangbo & Zhao, Mofei, 2023. "Global manipulation by local obfuscation," Journal of Economic Theory, Elsevier, vol. 207(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wrk:wcreta:22. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Margaret Nash (email available below). General contact details of provider: https://edirc.repec.org/data/dewaruk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.