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.
Publié le : 2005-05-14
Classification:
Capacities,
Choquet integral,
strong law of large numbers,
contents,
measures,
outer measures,
strong theorems,
28A12,
60F15
@article{1115386722,
author = {Maccheroni, Fabio and Marinacci, Massimo},
title = {A strong law of large numbers for capacities},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 1171-1178},
language = {en},
url = {http://dml.mathdoc.fr/item/1115386722}
}
Maccheroni, Fabio; Marinacci, Massimo. A strong law of large numbers for capacities. Ann. Probab., Tome 33 (2005) no. 1, pp. 1171-1178. http://gdmltest.u-ga.fr/item/1115386722/