Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)

Contrary to the finite dimensional set-up, the hypothesis of an atomless measure space of traders does not entail convexity of aggregate demand sets if there are infinitely many commodities. In this paper an assumption is introduced which sharpens the non-atomicity hypothesis by requiring that there are "many agents of every type." When this condition holds, aggregate demand in an infinite dimensional setting becomes convex even if individual preferences are non-convex. This result is applied to prove the existence of competitive equilibria in such a context.