Learning.measurable_uncurry_sumRewards'🔗

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.measurable_uncurry_sumRewards'.{u_1} {𝓐 : Type u_1}
  {m𝓐 : MeasurableSpace 𝓐} [DecidableEq 𝓐] [MeasurableEq 𝓐] (n : ℕ) :
  Measurable fun p => sumRewards' n (Prod.fst p) (Prod.snd p)
Learning.measurable_uncurry_sumRewards'.{u_1}
  {𝓐 : Type u_1} {m𝓐 : MeasurableSpace 𝓐}
  [DecidableEq 𝓐] [MeasurableEq 𝓐]
  (n : ℕ) :
  Measurable fun p =>
    sumRewards' n (Prod.fst p)
      (Prod.snd p)

lemma measurable_uncurry_sumRewards' [MeasurableEq 𝓐] (n : ℕ) :
    Measurable (fun p : (Iic n → 𝓐 × ℝ) × 𝓐 ↦ sumRewards' n p.1 p.2)

by
  simp_rw [sumRewards']
  have h_meas s : Measurable (fun p : (Iic n → 𝓐 × ℝ) × 𝓐 ↦
      if (p.1 s).1 = p.2 then (p.1 s).2 else 0) := by
    refine Measurable.ite ?_ (by fun_prop) (by fun_prop)
    exact measurableSet_eq_fun (by fun_prop) (by fun_prop)
  fun_prop

Dependency graph

Type dependencies (1)

Learning.sumRewards'.{u_1} {𝓐 : Type u_1} [DecidableEq 𝓐] (n : ℕ)
  (h : ↥(Finset.Iic n) → 𝓐 × ℝ) (a : 𝓐) : ℝ
Learning.sumRewards'.{u_1} {𝓐 : Type u_1}
  [DecidableEq 𝓐] (n : ℕ)
  (h : ↥(Finset.Iic n) → 𝓐 × ℝ) (a : 𝓐) :
  ℝ

noncomputable
def sumRewards' (n : ℕ) (h : Iic n → 𝓐 × ℝ) (a : 𝓐) :=
  ∑ s, if (h s).1 = a then (h s).2 else 0