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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 | import Mathlib
namespace OAI
namespace Invariant233.CouplingMarginalBounds
open MeasureTheory
noncomputable def rho (κ m w : ℝ) : ℝ := κ * Real.sqrt (w / m)
noncomputable def diagonalMass (κ m a b t : ℝ) : ℝ :=
1 - 2 * rho κ m a - 2 * rho κ m b - t / m
noncomputable def uniformDensity {Ω : Type*} [MeasurableSpace Ω]
(μ : Measure Ω) (s : Set Ω) : Ω → ℝ :=
s.indicator (fun _ => (μ.real s)⁻¹)
noncomputable def componentProbabilities (κ m a b t : ℝ) : Fin 5 → ℝ :=
![rho κ m a, rho κ m a, rho κ m b, rho κ m b, t / m]
noncomputable def componentVarianceBounds (m a b : ℝ) : Fin 5 → ℝ :=
![2 / a, 2 / a, 2 / b, 2 / b, m]
end Invariant233.CouplingMarginalBounds
end OAI
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