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Learning.IT.hist_eq_frestrictLe🔗

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Minimal Lean file

hist_eq_frestrictLe🔗

LemmaLearning.IT.hist_eq_frestrictLe
Details

No docstring.

🔗theorem
Learning.IT.hist_eq_frestrictLe.{u_1, u_2} {𝓐 : Type u_1}
  {𝓨 : Type u_2} : hist = Preorder.frestrictLe
Learning.IT.hist_eq_frestrictLe.{u_1, u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2} :
  hist = Preorder.frestrictLe

Code

lemma hist_eq_frestrictLe :
    hist = Preorder.frestrictLe («π»
Type uses (1)
Used by (1)

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Proof
fun _ ↦ 𝓐 × 𝓨) := by
  ext n h i : 3
  simp [hist, Preorder.frestrictLe]

Dependency graph

Type dependencies (1)

hist🔗

DefinitionLearning.IT.hist
Details

hist n is the history up to time n. This is a random variable on the measurable space ℕ → 𝓐 × 𝓨.

🔗def
Learning.IT.hist.{u_1, u_2} {𝓐 : Type u_1} {𝓨 : Type u_2} (n : ℕ)
  (h : ℕ → 𝓐 × 𝓨) : ↥(Finset.Iic n) → 𝓐 × 𝓨
Learning.IT.hist.{u_1, u_2} {𝓐 : Type u_1}
  {𝓨 : Type u_2} (n : ℕ) (h : ℕ → 𝓐 × 𝓨) :
  ↥(Finset.Iic n) → 𝓐 × 𝓨

Code

def hist (n : ℕ) (h : ℕ → 𝓐 × 𝓨) : Iic n → 𝓐 × 𝓨 := fun i ↦ h i
Used by (23)

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