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0789dda | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | import Mathlib
namespace OAI
namespace SymmetricMahler
variable {I : Type*} [Fintype I]
def coordinatePolar (K : Set (I → ℝ)) : Set (I → ℝ) :=
{p | ∀ v ∈ K, (∑ i, p i*v i) ≤ 1}
noncomputable section
open Set MeasureTheory
theorem symmetric_mahler {n : ℕ} (hn : 1 ≤ n)
{K : Set (Fin n → ℝ)} (hK : IsCompact K) (hconv : Convex ℝ K)
(hsym : ∀ x ∈ K, -x ∈ K) (hint : (interior K).Nonempty) :
(4:ℝ)^n/(Nat.factorial n:ℝ) ≤
(volume K).toReal*(volume (coordinatePolar K)).toReal := by
sorry
end
end SymmetricMahler
end OAI
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