Gives a bound on how far the sum of a large number of possibly non-convex sets can be from being convex, showing the sum becomes nearly convex as the number of sets grows. Named for Lloyd Shapley and Jon Folkman, it has applications explaining approximate convexity phenomena in economic equilibrium theory.
Facts
StatementFor a finite collection of subsets of a finite-dimensional real vector space whose number exceeds the space's dimension, the Minkowski sum of the sets lies within a bounded distance of its own convex hull, so the sum becomes nearly convex even though none of the individual sets need be convex. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Shapley-Folkman Theorem (Wikipedia)
Wikimedia FoundationHistory section, opening sentenceQuote, History section, opening sentence
The lemma of Lloyd Shapley and Jon Folkman was first published by the economist Ross M. Starr, who was investigating the existence of economic equilibria while studying with Kenneth Arrow.
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