LeanMachineLearning exposition

Learning.IT.measurable_feedback🔗

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Minimal Lean file

measurable_feedback🔗

LemmaLearning.IT.measurable_feedback
Details

No docstring.

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

Code

lemma measurable_feedback (n : ℕ) : Measurable (feedback n (𝓐
Type uses (1)
Used by (9)

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

Dependency graph

Type dependencies (1)

feedback🔗

DefinitionLearning.IT.feedback
Details

feedback n is the feedback at time n. This is a random variable on the measurable space ℕ → 𝓐 × 𝓨.

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

Code

def feedback (n : ℕ) (h : ℕ → 𝓐 × 𝓨) : 𝓨 := (h n).2
Used by (16)

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