Bandits.ArrayModel.measurable_pullCount_action_add_one_hist🔗

Bandits.ArrayModel.measurable_pullCount_action_add_one_hist.{u_1, u_2}
  {𝓐 : Type u_1} {R : Type u_2} {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R} [Nonempty 𝓐] [StandardBorelSpace 𝓐]
  [DecidableEq 𝓐] (alg : Learning.Algorithm 𝓐 R) (n : ℕ) :
  Measurable fun ω =>
    Learning.pullCount (action alg) (action alg (n + 1) ω) (n + 1) ω
Bandits.ArrayModel.measurable_pullCount_action_add_one_hist.{u_1,
    u_2}
  {𝓐 : Type u_1} {R : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R} [Nonempty 𝓐]
  [StandardBorelSpace 𝓐] [DecidableEq 𝓐]
  (alg : Learning.Algorithm 𝓐 R) (n : ℕ) :
  Measurable fun ω =>
    Learning.pullCount (action alg)
      (action alg (n + 1) ω) (n + 1) ω

lemma measurable_pullCount_action_add_one_hist (alg : Algorithm 𝓐 R) (n : ℕ) :
    Measurable[MeasurableSpace.comap (fun ω ↦ (action alg (n + 1) ω, hist alg ω n)) inferInstance]
      (fun ω ↦ pullCount (action alg) (action alg (n + 1) ω) (n + 1) ω)

by
  simp_rw [pullCount_eq_sum]
  refine measurable_sum _ fun i hi ↦ Measurable.ite ?_ (by fun_prop) (by fun_prop)
  refine measurableSet_eq_fun ?_ (measurable_comp_comap _ measurable_fst)
  rw [measurable_iff_comap_le]
  simp_rw [hist_eq _ _ n]
  rw [← measurable_iff_comap_le]
  unfold action
  refine Measurable.fst (mγ := inferInstance) ?_
  have : (hist alg · i ⟨i, by grind⟩) =
      (fun ω : 𝓐 × (Iic n → 𝓐 × R) ↦ ω.2 ⟨i, by grind⟩) ∘
        (fun ω ↦ (action alg (n + 1) ω, fun i : Iic n ↦ hist alg ω i ⟨i, by grind⟩)) := rfl
  rw [this]
  exact measurable_comp_comap _ (Measurable.prodMk (by fun_prop) (by fun_prop))

Meaning last changed in v4.34.0-rc2-1-g439785b (2026-08-23), the 5th recorded change.

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.

Dependency graph

Audit surface: 10 project declarations, 79 external constants

✓ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.