Learning.IT.measurable_feedback_prod🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

Learning.IT.measurable_feedback_prod.{u_1, u_2} {𝓐 : Type u_1}
  {𝓨 : Type u_2} {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} :
  Measurable fun p => feedback (Prod.fst p) (Prod.snd p)
Learning.IT.measurable_feedback_prod.{u_1,
    u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} :
  Measurable fun p =>
    feedback (Prod.fst p) (Prod.snd p)

lemma measurable_feedback_prod : Measurable (fun p : ℕ × (ℕ → 𝓐 × 𝓨) ↦ feedback p.1 p.2)

measurable_from_prod_countable_right fun n ↦ (by simp only; fun_prop)

Dependency graph

Type dependencies (1)

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

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