import OAI.Probability.GaussianReplacement.StreamGeometry
import OAI.Probability.GaussianRegression.ReplicaMoments

namespace OAI

open MeasureTheory ProbabilityTheory Set Filter
open scoped ENNReal NNReal RealInnerProductSpace Topology
noncomputable section
universe u
namespace NoiselessRegression

open InnerProductSpace

section GramFactorization
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
  {ι : Type*} [Fintype ι]

variable (n : ℕ)

end GramFactorization

section GramDistances
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
  [FiniteDimensional ℝ E] {n : ℕ}

variable [MeasurableSpace E] [BorelSpace E]

end GramDistances

section PiLast
variable {E : Type*} [MeasurableSpace E] {n : ℕ} (ν : Measure E) [SigmaFinite ν]

end PiLast

section ReplicaMoments
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
  [FiniteDimensional ℝ E] [MeasurableSpace E] [BorelSpace E]

end ReplicaMoments
section AePiLast
variable {E : Type*} [MeasurableSpace E] {n : ℕ} (ν : Measure E) [SigmaFinite ν]

end AePiLast

section ReplicaNondegenerate
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
  [FiniteDimensional ℝ E] [MeasurableSpace E] [BorelSpace E]

end ReplicaNondegenerate

end NoiselessRegression

end

end OAI