A strong law of large numbers for capacities

Details A strong law of large numbers for capacities A strong law of large numbers for capacities

2005-06-29

arxiv.org/abs/math/0506597v1

Annals of Probability 2005, Vol. 33, No. 3, 1171-1178

Mathematics

Probability

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

Scientific paper

10.1214/009117904000001062

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.

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