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A strong law of large numbers for capacities

Author

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  • Fabio Maccheroni
  • Massimo Marinacci

Abstract

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.

Suggested Citation

  • Fabio Maccheroni & Massimo Marinacci, 2004. "A strong law of large numbers for capacities," ICER Working Papers - Applied Mathematics Series 28-2004, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:28-2004
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2004/Maccheroni-Marinacci28-04.pdf
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    Citations

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    Cited by:

    1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    2. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    3. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.

    More about this item

    Keywords

    Capacities; Choquet integral; Strong law of large numbers;
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