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Learning.measurable_trajectory🔗

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measurable_trajectory🔗

LemmaLearning.measurable_trajectory
Details

No docstring.

🔗theorem
Learning.measurable_trajectory.{u_1, u_2, u_3} {𝓐 : Type u_1}
  {𝓨 : Type u_2} {Ω : Type u_3} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} {mΩ : MeasurableSpace Ω} {A : ℕ → Ω → 𝓐}
  {Y : ℕ → Ω → 𝓨} (hA : ∀ (n : ℕ), Measurable (A n))
  (hR : ∀ (n : ℕ), Measurable (Y n)) : Measurable (trajectory A Y)
Learning.measurable_trajectory.{u_1, u_2,
    u_3}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ω : Type u_3} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨}
  {mΩ : MeasurableSpace Ω} {A : ℕ → Ω → 𝓐}
  {Y : ℕ → Ω → 𝓨}
  (hA : ∀ (n : ℕ), Measurable (A n))
  (hR : ∀ (n : ℕ), Measurable (Y n)) :
  Measurable (trajectory A Y)

Code

lemma measurable_trajectory {A : ℕ → Ω → 𝓐} {Y : ℕ → Ω → 𝓨} (hA : ∀ n, Measurable (A n))
    (hR : ∀ n, Measurable (Y n)) : Measurable (trajectory A Y)
Type uses (1)
Used by (8)

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Proof
by
  unfold trajectory
  fun_prop

Dependency graph

Type dependencies (1)

trajectory🔗

DefinitionLearning.trajectory
Details

A random variable that gives the sequence of action-feedback pairs.

🔗def
Learning.trajectory.{u_1, u_2, u_3} {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ω : Type u_3} (A : ℕ → Ω → 𝓐) (Y : ℕ → Ω → 𝓨) (ω : Ω) : ℕ → 𝓐 × 𝓨
Learning.trajectory.{u_1, u_2, u_3}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ω : Type u_3} (A : ℕ → Ω → 𝓐)
  (Y : ℕ → Ω → 𝓨) (ω : Ω) : ℕ → 𝓐 × 𝓨

Code

def trajectory (A : ℕ → Ω → 𝓐) (Y : ℕ → Ω → 𝓨) (ω : Ω) : ℕ → 𝓐 × 𝓨 := fun n ↦ (A n ω, Y n ω)
Used by (18)

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