LeanMachineLearning

Learning.IsAlgEnvSeq.filtrationπŸ”—

Definition

Filtration generated by the history up to time n.

πŸ”—def
Learning.IsAlgEnvSeq.filtration.{u_1, u_2, u_3} {𝓐 : Type u_1}
  {𝓨 : Type u_2} {Ξ© : Type u_3} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} {mΞ© : MeasurableSpace Ξ©} {A : β„• β†’ Ξ© β†’ 𝓐}
  {Y : β„• β†’ Ξ© β†’ 𝓨} {alg : Algorithm 𝓐 𝓨} {env : Environment 𝓐 𝓨}
  {P : MeasureTheory.Measure Ξ©} [MeasureTheory.IsFiniteMeasure P]
  (h : IsAlgEnvSeq A Y alg env P) : MeasureTheory.Filtration β„• mΞ©
Learning.IsAlgEnvSeq.filtration.{u_1, u_2,
    u_3}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ξ© : Type u_3} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨}
  {mΞ© : MeasurableSpace Ξ©} {A : β„• β†’ Ξ© β†’ 𝓐}
  {Y : β„• β†’ Ξ© β†’ 𝓨} {alg : Algorithm 𝓐 𝓨}
  {env : Environment 𝓐 𝓨}
  {P : MeasureTheory.Measure Ξ©}
  [MeasureTheory.IsFiniteMeasure P]
  (h : IsAlgEnvSeq A Y alg env P) :
  MeasureTheory.Filtration β„• mΞ©

Code

def filtration (h : IsAlgEnvSeq A Y alg env P) : Filtration β„• mΞ© where seq i := MeasurableSpace.comap (history A Y i) inferInstance mono' i j hij := by simp only rw [← measurable_iff_comap_le] have : history A Y i = (fun h k ↦ h ⟨k.1, by grind⟩) ∘ history A Y j := rfl rw [this] exact measurable_comp_comap _ (by fun_prop) le' i := by rw [← measurable_iff_comap_le] exact Learning.measurable_history h.measurable_action h.measurable_feedback i

Actions: Source Β· Open Issue

Meaning last changed in v4.34.0-rc2-2-g4830b8c (2026-08-23).

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: 4 project declarations, 43 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.