English: The Shapley–Folkman lemma. The sixteen dark red points on the right are the Minkowski sum of the four nonconvex sets on the left, each of which consists of a pair of red points. The plus sign marks a point belonging to the (shaded) convex hull of the Minkowski sum; according to the lemma, this point may be represented as a sum of four points, one for each term in the Minkowski sum. Because the ambient space is two-dimensional, two of these four points belong to the convex hulls of their summands, and the remaining two belong to the summands themselves.