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9eeb9c7 | 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 28 29 30 | import OAI.Analysis.IntegralMeans.Model
import OAI.Analysis.IntegralMeans.Koebe
namespace OAI
noncomputable section
open Set MeasureTheory
open scoped ENNReal
namespace Brennan.Sharp
def koebeDomain : Set ℂ := koebeMap '' disk
def koebeInverse : ℂ → ℂ := Function.invFunOn koebeMap disk
def areaMoment (f : ℂ → ℂ) (U : Set ℂ) (t : ℝ) : ℝ≥0∞ :=
∫⁻ z in U, ENNReal.ofReal (‖deriv f z‖ ^ t) ∂volume
def SharpEndpointStatement : Prop :=
Schlicht koebeMap ∧
areaMoment koebeMap disk (-2) = ⊤ ∧
areaMoment koebeMap disk (2 / 3) = ⊤ ∧
¬ IntegrableOn (fun z => ‖deriv koebeInverse z‖ ^ (4 : ℝ)) koebeDomain volume ∧
¬ IntegrableOn (fun z => ‖deriv koebeInverse z‖ ^ (4 / 3 : ℝ)) koebeDomain volume
end Brennan.Sharp
end
end OAI
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