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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 31 32 | import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import OAI.Analysis.IrrationalRotation.Model.UnrestrictedDiagonal
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.MeasureTheory.Measure.Map
namespace OAI
open MeasureTheory
open scoped NNReal
noncomputable section
namespace Invariant233
instance sequenceHilbertIntMeasurableSpace : MeasurableSpace (SequenceHilbert ℤ) := borel _
instance sequenceHilbertIntBorelSpace : BorelSpace (SequenceHilbert ℤ) := ⟨rfl⟩
def UniformlyAbsolutelyContinuous {X ι : Type*} [MeasurableSpace X]
(μ : Measure X) (ν : ι → Measure X) : Prop :=
∀ ε : ℝ≥0, 0 < ε → ∃ δ : ℝ≥0, 0 < δ ∧
∀ A : Set X, MeasurableSet A → μ A < δ → ∀ i, ν i A < ε
noncomputable def ratioDiagonal {X : Type*} (F : ℤ → X → ℝ) (t : X × X) :
SequenceHilbert ℤ →L[ℂ] SequenceHilbert ℤ :=
SequenceHilbert.boundedDiagonal (fun i => ((F i t.2 / F i t.1 : ℝ) : ℂ))
end Invariant233
end
end OAI
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