It is known that in large economies with strongly convex preferences, the commodity bundles agents receive at core allocations are near their demand sets. Without convexity, it is know that agents need not be near their demand sets, although they will satisfy a weaker condition. In this paper, we show that, for “most” economies (in the sense of probability and in the sense of the Baire category theorem), the stronger form of approximation holds without convexity.