The Annals of Probability

A strong law of large numbers for capacities

Fabio Maccheroni and Massimo Marinacci

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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.

Article information

Source
Ann. Probab. Volume 33, Number 3 (2005), 1171-1178.

Dates
First available in Project Euclid: 6 May 2005

Permanent link to this document
http://projecteuclid.org/euclid.aop/1115386722

Digital Object Identifier
doi:10.1214/009117904000001062

Mathematical Reviews number (MathSciNet)
MR2135316

Zentralblatt MATH identifier
02182593

Subjects
Primary: 28A12: Contents, measures, outer measures, capacities 60F15: Strong theorems

Keywords
Capacities Choquet integral strong law of large numbers contents measures outer measures strong theorems

Citation

Maccheroni, Fabio; Marinacci, Massimo. A strong law of large numbers for capacities. Ann. Probab. 33 (2005), no. 3, 1171--1178. doi:10.1214/009117904000001062. http://projecteuclid.org/euclid.aop/1115386722.


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