Bandits.ArrayModel.measurable_action_add_one_truePast🔗

Bandits.ArrayModel.measurable_action_add_one_truePast.{u_1, u_2}
  {𝓐 : Type u_1} {R : Type u_2} {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R} [Nonempty 𝓐] [StandardBorelSpace 𝓐]
  [DecidableEq 𝓐] [Nonempty R] [Countable 𝓐]
  (alg : Learning.Algorithm 𝓐 R) (a : 𝓐) (n : ℕ) :
  Measurable (action alg (n + 1))
Bandits.ArrayModel.measurable_action_add_one_truePast.{u_1,
    u_2}
  {𝓐 : Type u_1} {R : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R} [Nonempty 𝓐]
  [StandardBorelSpace 𝓐] [DecidableEq 𝓐]
  [Nonempty R] [Countable 𝓐]
  (alg : Learning.Algorithm 𝓐 R) (a : 𝓐)
  (n : ℕ) :
  Measurable (action alg (n + 1))

lemma measurable_action_add_one_truePast [Countable 𝓐] (alg : Algorithm 𝓐 R)
    (a : 𝓐) (n : ℕ) :
    Measurable[MeasurableSpace.comap (truePast alg a n) inferInstance]
      (action alg (n + 1))

by
  rw [action_add_one_eq]
  change Measurable[MeasurableSpace.comap (truePast alg a n) inferInstance]
    ((fun p ↦ algFunction alg n p.1 p.2) ∘ (fun ω ↦ (hist alg ω n, ω.1 (n + 1))))
  refine (measurable_algFunction alg n).comp (Measurable.prodMk ?_ ?_)
  · exact measurable_hist_truePast alg a n
  · have : (fun ω ↦ ω.1 (n + 1)) =
      (fun (p : probSpace 𝓐 R) ↦ p.1 (n + 1)) ∘ (truePast alg a n) := rfl
    rw [this]
    exact Measurable.comp (by fun_prop) (Measurable.of_comap_le le_rfl)

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: 12 project declarations, 100 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.