Theorems · Theorem · probability

MeasureTheory.condExp_stopping_time_ae_eq_restrict_eq_of_countable

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : LinearOrder ι] {μ : MeasureTheory.Measure Ω}
  {ℱ : MeasureTheory.Filtration ι m} {τ : Ω → WithTop ι} {E : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace ℝ E] [CompleteSpace E] {f : Ω → E} [Countable ι] [MeasureTheory.SigmaFiniteFiltration μ ℱ]
  (hτ : MeasureTheory.IsStoppingTime ℱ τ) [MeasureTheory.SigmaFinite (μ.trim ⋯)] (i : ι),
  μ[f | hτ.measurableSpace] =ᵐ[μ.restrict {x | τ x = ↑i}] μ[f | ↑ℱ i]

Defined in

Mathlib.Probability.Process.Stopping

Cited by

0 results in Mathlib

Foundations

Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderNormedAddCommGroupNormedSpaceCompleteSpaceCountableMeasureTheory.SigmaFiniteFiltrationMeasureTheory.SigmaFinite