A strong law of large numbers for capacities

• 成果类型: Article
• 署名作者: Maccheroni, F; Marinacci, M
• 署名单位: Bocconi University; Bocconi University; University of Turin; University of Turin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000001062
• 发表日期: 2005
• 页码: 1171-1178
• 关键词: lower probabilities; Random Sets

摘要

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.