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Learning.IT.measurable_hist🔗

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Minimal Lean file

measurable_hist🔗

LemmaLearning.IT.measurable_hist
Details

No docstring.

🔗theorem
Learning.IT.measurable_hist.{u_1, u_2} {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} (n : ℕ) :
  Measurable (hist n)
Learning.IT.measurable_hist.{u_1, u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} (n : ℕ) :
  Measurable (hist n)

Code

lemma measurable_hist (n : ℕ) : Measurable (hist n (𝓐
Type uses (1)
Used by (5)

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Proof
𝓐) (𝓨 := 𝓨)) := by unfold hist; fun_prop

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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