`Bandits.iIndepFun_eval_streamMeasure''`🔗

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Minimal Lean file

`iIndepFun_eval_streamMeasure''`🔗

LemmaBandits.iIndepFun_eval_streamMeasure''

Details

No docstring.

theorem

Bandits.iIndepFun_eval_streamMeasure''.{u_1, u_2} {𝓐 : Type u_1}
  {R : Type u_2} {m𝓐 : MeasurableSpace 𝓐} {mR : MeasurableSpace R}
  (ν : ProbabilityTheory.Kernel 𝓐 R)
  [ProbabilityTheory.IsMarkovKernel ν] (a : 𝓐) :
  ProbabilityTheory.iIndepFun (fun n ω => ω n a) (streamMeasure ν)
Bandits.iIndepFun_eval_streamMeasure''.{u_1,
    u_2}
  {𝓐 : Type u_1} {R : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R}
  (ν : ProbabilityTheory.Kernel 𝓐 R)
  [ProbabilityTheory.IsMarkovKernel ν]
  (a : 𝓐) :
  ProbabilityTheory.iIndepFun
    (fun n ω => ω n a) (streamMeasure ν)

Code

lemma iIndepFun_eval_streamMeasure'' (ν : Kernel 𝓐 R) [IsMarkovKernel ν] (a : 𝓐) :
    iIndepFun (fun n ω ↦ ω n a) (streamMeasure ν)

Type uses (1)

streamMeasure

Body uses (1)

iIndepFun_eval_streamMeasure'

Used by (5)

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Proof

(iIndepFun_eval_streamMeasure' ν).comp (g := fun i ω ↦ ω a) (by fun_prop)

Dependency graph

Type dependencies (1)

`streamMeasure`🔗

DefinitionBandits.streamMeasure

Details

Measure of an infinite stream of rewards from each action.

def

Bandits.streamMeasure.{u_1, u_2} {𝓐 : Type u_1} {R : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐} {mR : MeasurableSpace R}
  (ν : ProbabilityTheory.Kernel 𝓐 R) : MeasureTheory.Measure (ℕ → 𝓐 → R)
Bandits.streamMeasure.{u_1, u_2}
  {𝓐 : Type u_1} {R : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {mR : MeasurableSpace R}
  (ν : ProbabilityTheory.Kernel 𝓐 R) :
  MeasureTheory.Measure (ℕ → 𝓐 → R)

Code

noncomputable
def streamMeasure (ν : Kernel 𝓐 R) : Measure (ℕ → 𝓐 → R) :=
  Measure.infinitePi fun _ ↦ Measure.infinitePi ν

Used by (56)

Actions: Source · Open Issue

Bandits.iIndepFun_eval_streamMeasure''🔗

iIndepFun_eval_streamMeasure''🔗

streamMeasure🔗

`Bandits.iIndepFun_eval_streamMeasure''`🔗

`iIndepFun_eval_streamMeasure''`🔗

`streamMeasure`🔗