A strong law of large numbers for capacities

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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.
Published at http://dx.doi.org/10.1214/009117904000001062 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Probability, 28A12, 60F15. (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/75619

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506597
 http://arxiv.org/abs/math/0506597
 Annals of Probability 2005, Vol. 33, No. 3, 1171-1178
 doi:10.1214/009117904000001062

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arXiv