leanprover-community/mathlib4

The Shapley-Folkman lemma

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#14,427 opened on Jul 4, 2024

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good first issuet-analysis

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Description

The Shapley-Folkman lemma is a convex analysis result standard in the economics literature. In contrast, it is basically unheard of in mathematics.

The proof is elementary, and very similar to the proofs of Carathéodory's and Radon's theorems, which should serve as inspiration.

This issue existed in mathlib3 as https://github.com/leanprover-community/mathlib/issues/18135.

Contributor guide

Research direction
Study Carathéodory's and Radon's theorem proofs, then adapt the approach using convex analysis to formalize the Shapley Folkman lemma.
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Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-3 hours
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
Active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
Clear
Prerequisites
Lean
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
70