Convex hull Shapley–Folkman lemma

in convex hull of red set, each blue point convex combination of red points.

for every subset q of real vector space, convex hull conv(q) minimal convex set contains q. thus conv(q) intersection of convex sets cover q. convex hull of set can equivalently defined set of convex combinations of points in q. example, convex hull of set of integers {0,1} closed interval of real numbers [0,1], contains integer end-points. convex hull of unit circle closed unit disk, contains unit circle.