The main theorem in this paper is one in a long series of theorems which show the existence of equilibrium in economies without convex preferences, without convex consumption sets, or without complete and transitive preorderings. Here, it is proved that a competitive equilibrium exists in a large economy with not necessarily convex consumption sets and where preferences are continuous and transitive. As an additional assumption the continuity of the wealth distribution with respect to the Borel-Lebesque measure is required.