LeanMachineLearning

Bandits.ArrayModel.measurable_pullCount_add_one_truePastπŸ”—

Lemma

No docstring.

πŸ”—theorem
Bandits.ArrayModel.measurable_pullCount_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 : β„•) :
  Measurable (Learning.pullCount (action alg) a (n + 1))
Bandits.ArrayModel.measurable_pullCount_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 : β„•) :
  Measurable
    (Learning.pullCount (action alg) a
      (n + 1))

Code

lemma measurable_pullCount_add_one_truePast [Countable 𝓐] (alg : Algorithm 𝓐 R) (a : 𝓐) (n : β„•) :
    Measurable[MeasurableSpace.comap (truePast alg a n) inferInstance]
      (pullCount (action alg) a (n + 1))
Proof
by
  change Measurable[MeasurableSpace.comap (truePast alg a n) inferInstance]
    (fun Ο‰ ↦ pullCount (action alg) a (n + 1) Ο‰)
  simp_rw [pullCount_eq_sum]
  refine measurable_sum _ fun i hi ↦ Measurable.ite ?_ (by fun_prop) (by fun_prop)
  refine (measurableSet_singleton _).preimage ?_
  have h_meas := measurable_hist_truePast alg a n
  simp_rw [hist_eq _ _ n, @measurable_pi_iff] at h_meas
  exact (h_meas ⟨i, by grind⟩).fst

Actions: Source Β· Open Issue

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 Β· open it in the Lean web editor.

Dependency graph

Audit surface: 12 project declarations, 101 external constants

βœ“ 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.