Summary: We propose an alternative assumption for the integral representation of the value function of P. Milgrom and I. Segal [Econometrica 70, No. 2, 583–601 (2002; Zbl 1103.90400)]. Instead of requiring that the utility function has a derivative almost everywhere, we impose that it has derivatives in all its domain. The idea is to obtain conditions in order to apply the Lebesgue theorem which provides at the same time an absolutely continuous value function and its integral representation. Our assumption is technically stronger than that of Milgrom and Segal but we argue that there is a substantial gain of economic interpretation in adding it. While it is difficult to interpret absolute continuity in terms of agent’s preferences, the existence of the derivative everywhere means that all agent’s choices are smooth.