A strong law of large numbers for capacities
Probability
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0506597,
title = {A strong law of large numbers for capacities},
author = {Fabio Maccheroni and Massimo Marinacci},
journal= {arXiv preprint arXiv:math/0506597},
year = {2007}
}
Comments
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)