In investigations where the parameter of interest is the mean or expectation of some random variable and the underlying probability measure (distribution) is unknown, one usually appeals to the central limit theorem, provided it holds. In this article the central limit theorem and the weak law of large numbers for capacities are presented. Capacities are non-additive probability measures which provide alternative and plausible measures of likelihood or uncertainty when the assumption of additivity is suspect. Some examples of practical problems in game theory, economics and finance that can be solved at least partially, by the central limit theorem for capacities, are presented.
