`Learning.measurable_pullCount`🔗

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

`measurable_pullCount`🔗

LemmaLearning.measurable_pullCount

Details

No docstring.

theorem

Learning.measurable_pullCount.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  {m𝓐 : MeasurableSpace 𝓐} {mΩ : MeasurableSpace Ω} [DecidableEq 𝓐]
  {A : ℕ → Ω → 𝓐} [MeasurableSingletonClass 𝓐]
  (hA : ∀ (n : ℕ), Measurable (A n)) (a : 𝓐) (t : ℕ) :
  Measurable fun ω => pullCount A a t ω
Learning.measurable_pullCount.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  {m𝓐 : MeasurableSpace 𝓐}
  {mΩ : MeasurableSpace Ω} [DecidableEq 𝓐]
  {A : ℕ → Ω → 𝓐}
  [MeasurableSingletonClass 𝓐]
  (hA : ∀ (n : ℕ), Measurable (A n))
  (a : 𝓐) (t : ℕ) :
  Measurable fun ω => pullCount A a t ω

Code

lemma measurable_pullCount [MeasurableSingletonClass 𝓐] (hA : ∀ n, Measurable (A n))
    (a : 𝓐) (t : ℕ) :
    Measurable (fun ω : Ω ↦ pullCount A a t ω)

Type uses (1)

pullCount

Body uses (1)

pullCount_eq_sum

Used by (15)

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Proof

by
  simp_rw [pullCount_eq_sum]
  have h_meas s : Measurable (fun ω : Ω ↦ if A s ω = a then 1 else 0) := by
    refine Measurable.ite ?_ (by fun_prop) (by fun_prop)
    exact (measurableSet_singleton _).preimage (by fun_prop)
  fun_prop

Dependency graph

Type dependencies (1)

`pullCount`🔗

DefinitionLearning.pullCount

Details

Number of times action a was chosen up to time t (excluding t).

def

Learning.pullCount.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ
Learning.pullCount.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐)
  (t : ℕ) (ω : Ω) : ℕ

Code

noncomputable
def pullCount (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ :=
  #(filter (fun s ↦ A s ω = a) (range t))

Used by (146)

Actions: Source · Open Issue

Learning.measurable_pullCount🔗

measurable_pullCount🔗

pullCount🔗

`Learning.measurable_pullCount`🔗

`measurable_pullCount`🔗

`pullCount`🔗