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May 2005 A strong law of large numbers for capacities
Fabio Maccheroni, Massimo Marinacci
Ann. Probab. 33(3): 1171-1178 (May 2005). DOI: 10.1214/009117904000001062

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.

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Fabio Maccheroni. Massimo Marinacci. "A strong law of large numbers for capacities." Ann. Probab. 33 (3) 1171 - 1178, May 2005. https://doi.org/10.1214/009117904000001062

Information

Published: May 2005
First available in Project Euclid: 6 May 2005

zbMATH: 1074.60041
MathSciNet: MR2135316
Digital Object Identifier: 10.1214/009117904000001062

Subjects:
Primary: 28A12 , 60F15

Keywords: Capacities , Choquet integral , contents , Measures , outer measures , Strong law of large numbers , strong theorems

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 3 • May 2005
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