Theorems · Theorem · probability

MeasureTheory.measurableSet_preimage_stoppedValue_inter

∀ {Ω : Type u_1} {β : Type u_2} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : Nonempty ι] {u : ι → Ω → β}
  {τ : Ω → WithTop ι} [inst_1 : LinearOrder ι] [inst_2 : MeasurableSpace ι] [inst_3 : TopologicalSpace ι]
  [OrderTopology ι] [SecondCountableTopology ι] [BorelSpace ι] [inst_7 : TopologicalSpace β]
  {f : MeasureTheory.Filtration ι m} [TopologicalSpace.PseudoMetrizableSpace β] [inst_9 : MeasurableSpace β]
  [BorelSpace β],
  MeasureTheory.IsStronglyProgressive f u →
    MeasureTheory.IsStoppingTime f τ →
      ∀ {t : Set β}, MeasurableSet t → ∀ (i : ι), MeasurableSet (MeasureTheory.stoppedValue u τ ⁻¹' t ∩ {ω | τ ω ≤ ↑i})

Defined in

Mathlib.Probability.Process.Stopping

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonemptyLinearOrderMeasurableSpaceTopologicalSpaceOrderTopologySecondCountableTopologyBorelSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceMeasurableSpaceBorelSpace