Theorems · Theorem · probability
MeasureTheory.IsStoppingTime.measurableSet_inter_le_iff
∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : LinearOrder ι] {f : MeasureTheory.Filtration ι m}
{τ π : Ω → WithTop ι} [inst_1 : TopologicalSpace ι] [SecondCountableTopology ι] [OrderTopology ι]
(hτ : MeasureTheory.IsStoppingTime f τ) (hπ : MeasureTheory.IsStoppingTime f π) (s : Set Ω),
MeasurableSet (s ∩ {ω | τ ω ≤ π ω}) ↔ MeasurableSet (s ∩ {ω | τ ω ≤ π ω})- Defined in
- Mathlib.Probability.Process.Stopping
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- WithTopstatement and proof · cited by 3,754
- MeasurableSetstatement and proof · cited by 3,075
- OrderTopologystatement and proof · cited by 1,355
- SecondCountableTopologystatement and proof · cited by 750
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.IsStoppingTimestatement and proof · cited by 122
- Set.inter_assocproof · cited by 67
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.IsStoppingTime.measurableSet_stopping_time_le_minproof · cited by 2
- MeasureTheory.condExp_min_stopping_time_ae_eq_restrict_leproof · cited by 1