The concave integral for capacities

Choquet integral [1] was the first to deal with integration according to a capacity. Choquet introduced an integral which coincides with that of Lebesgue when the capacity is additive. Lehrer [3] presented a concave integral, which differs from the Choquet integral, and characterized it when the underlying space is finite. The concave and the Choquet integrals coincide when the capacity is convex (supermodular). The paper [4] investigates the concave integral when the underlying space is general. We here bring the basic definitions, questions asked and some of the results obtained.