Sequentially continuous non-monotonic choquet integrals

Schmeidler (Proc. Amer. Math. Soc. 97 (2) (1986) 255-261) established an integral representation theorem through the Choquet integral for functionals satisfying monotonicity and a weaker condition than additivity, namely comonotonic additivity. Murofushi-Sugeno-Machida (Fuzzy Sets and Systems 64 (1994) 73-86) generalize this representation to the case of bounded variation functionals omitting the monotonicity condition. We give an alternative approach which is based on sequential continuity and tolerates non-monotonicity. This later condition is equivalent to σ-additivity in measure theory.