On Independence for Capacities with Law of Large Numbers

Weihuan Huang

Published 2017-12-09Version 1

This paper introduces new notions of Fubini independence and Exponential independence of random variables under capacities to fit Ellsberg's model, and finds out the relationships between Fubini independence, Exponential independence, MacCheroni and Marinacci's independence and Peng's independence. As an application, we give a weak law of large numbers for capacities under Exponential independence.