Before revision:  Under the assumption of the existence of consistent price systems, which makes the duality approach possible, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures.
After revision:  Under the assumption of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures.