`Learning.measurable_uncurry_pullCount_comp`🔗

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_uncurry_pullCount_comp`🔗

LemmaLearning.measurable_uncurry_pullCount_comp

Details

No docstring.

theorem

Learning.measurable_uncurry_pullCount_comp.{u_1, u_3} {𝓐 : Type u_1}
  {Ω : Type u_3} {m𝓐 : MeasurableSpace 𝓐} {mΩ : MeasurableSpace Ω}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} [Countable 𝓐]
  [MeasurableSingletonClass 𝓐] (hA : ∀ (n : ℕ), Measurable (A n))
  {f : Ω → 𝓐} (hf : Measurable f) {g : Ω → ℕ} (hg : Measurable g) :
  Measurable fun ω => pullCount A (f ω) (g ω) ω
Learning.measurable_uncurry_pullCount_comp.{u_1,
    u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  {m𝓐 : MeasurableSpace 𝓐}
  {mΩ : MeasurableSpace Ω} [DecidableEq 𝓐]
  {A : ℕ → Ω → 𝓐} [Countable 𝓐]
  [MeasurableSingletonClass 𝓐]
  (hA : ∀ (n : ℕ), Measurable (A n))
  {f : Ω → 𝓐} (hf : Measurable f)
  {g : Ω → ℕ} (hg : Measurable g) :
  Measurable fun ω =>
    pullCount A (f ω) (g ω) ω

Code

lemma measurable_uncurry_pullCount_comp [Countable 𝓐] [MeasurableSingletonClass 𝓐]
    (hA : ∀ n, Measurable (A n)) {f : Ω → 𝓐} (hf : Measurable f) {g : Ω → ℕ} (hg : Measurable g) :
    Measurable (fun ω ↦ pullCount A (f ω) (g ω) ω)

Type uses (1)

pullCount

Body uses (1)

measurable_pullCount

Used by (6)

Actions: Source · Open Issue

Proof

by
  change Measurable ((fun aω ↦ pullCount A aω.1 (g aω.2) aω.2) ∘ fun ω ↦ (f ω, ω))
  apply Measurable.comp _ (by fun_prop)
  refine measurable_from_prod_countable_right fun a ↦ ?_
  change Measurable ((fun tω ↦ pullCount A a tω.1 tω.2) ∘ fun ω ↦ (g ω, ω))
  apply Measurable.comp _ (by fun_prop)
  exact measurable_from_prod_countable_right (fun t ↦ measurable_pullCount hA a t)

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_uncurry_pullCount_comp🔗

measurable_uncurry_pullCount_comp🔗

pullCount🔗

`Learning.measurable_uncurry_pullCount_comp`🔗

`measurable_uncurry_pullCount_comp`🔗

`pullCount`🔗