Shapley-Folkman Theorem

The Shapley-Folkman Theorem explores how the sum of many small or non-convex sets (collections of points) behaves. It states that when you add together numerous such sets, the resulting combined set is close to being convex (a shape with no indentations) — especially if the number of sets is large relative to their non-convex parts. In simple terms, summing many "imperfect" sets produces a shape that looks increasingly like a smooth, convex shape, which simplifies analysis and optimization in complex situations.