The Induced Capacity and Choquet Integral Monotone Convergence

Given a probability measure over a state space, a partial collection (sub-σalgebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The induced capacity of an event F is the probability of the maximal (with respect to inclusion) event contained in F whose probability is known. The Choquet integral with respect to the induced capacity coincides with the integral with respect to a probability specified on a sub-algebra (Lehrer [7]). We study Choquet integral monotone convergence and apply the results to the integral with respect to the induced capacity. The paper characterizes the properties of sub-σ-algebras and of induced capacities which yield integral monotone convergence. JEL classification: D81.