Theorems · Theorem · probability

MeasureTheory.integrable_stoppedValue

∀ {Ω : Type u_1} (ι : Type u_3) {m : MeasurableSpace Ω} [inst : Nonempty ι] {μ : MeasureTheory.Measure Ω}
  {τ : Ω → WithTop ι} {E : Type u_4} {u : ι → Ω → E} [inst_1 : PartialOrder ι] {ℱ : MeasureTheory.Filtration ι m}
  [inst_2 : NormedAddCommGroup E] [LocallyFiniteOrderBot ι],
  MeasureTheory.IsStoppingTime ℱ τ →
    (∀ (n : ι), MeasureTheory.Integrable (u n) μ) →
      ∀ {N : ι}, (∀ (ω : Ω), τ ω ≤ ↑N) → MeasureTheory.Integrable (MeasureTheory.stoppedValue u τ) μ

Defined in

Mathlib.Probability.Process.Stopping

Cited by

3 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonemptyPartialOrderNormedAddCommGroupLocallyFiniteOrderBot