Theorems · Theorem · probability
MeasureTheory.measurable_stoppedValue
∀ {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 →
∀ (hτ : MeasureTheory.IsStoppingTime f τ), Measurable (MeasureTheory.stoppedValue u τ)- Defined in
- Mathlib.Probability.Process.Stopping
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Filter.Tendstoproof · cited by 3,814
- WithTopstatement and proof · cited by 3,754
- MeasurableSetproof · cited by 3,075
- Set.iUnionproof · cited by 2,483
- Filter.atTopproof · cited by 2,405
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Martingale.stoppedValue_min_ae_eq_condExpproof · cited by 0