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Source labels openChecked July 26, 2026

Green's Open ProblemsFunctional analysis

Ben Green's Open Problem 54

Let K⊂RnK \subset \mathbb{R}^n be a balanced compact set (that is, λK⊆K\lambda K \subseteq K whenever ∣λ∣≤1|\lambda| \leq 1) and suppose that the normalised Gaussian measure γn(K)≥0.99\gamma_n(K) \geq 0.99. Does 10K10K contain a compact convex set CC with $\gamma_n(C) \ge...

Functional analysisAMS 46AMS 52AMS 60

Mathematical statement

Let K⊂RnK \subset \mathbb{R}^n be a balanced compact set (that is, λK⊆K\lambda K \subseteq K whenever ∣λ∣≤1|\lambda| \leq 1) and suppose that the normalised Gaussian measure γn(K)≥0.99\gamma_n(K) \geq 0.99. Does 10K10K contain a compact convex set CC with γn(C)≥0.01\gamma_n(C) \geq 0.01?

Statement source: Green's Open Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

green_54

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem green_54 :    answer(sorry) ↔ ∀ K : Set (ℕ → ℝ), IsCompact K → Balanced ℝ K → (0.99 : ℝ≥0∞) ≤    gaussianMeasureInf K → ∃ C : Set (ℕ → ℝ), IsCompact C ∧ Convex ℝ C ∧ C ⊆ (10 : ℝ) • K ∧    (0.01 : ℝ≥0∞) ≤ gaussianMeasureInf C := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References

Pinned Formal Conjectures sourceformalizationBen Green's Open Problem 54background