  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 relations 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. Simulations show that Ellsberg's model enjoy the weak
law of large numbers when there is mean uncertainty with or without variance
uncertainty.
