Shapley-Folkman-type Theorem for Integrally Convex Sets

Abstract: The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete convex analysis.