| 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 | |