Theorems · Theorem · probability
MeasureTheory.IsStoppingTime.measurableSet_lt
∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : LinearOrder ι] {f : MeasureTheory.Filtration ι m}
{τ : Ω → WithTop ι} [inst_1 : TopologicalSpace ι] [OrderTopology ι] [FirstCountableTopology ι],
MeasureTheory.IsStoppingTime f τ → ∀ (i : ι), MeasurableSet {ω | τ ω < ↑i}- Defined in
- Mathlib.Probability.Process.Stopping
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- WithTopstatement and proof · cited by 3,754
- MeasurableSetstatement and proof · cited by 3,075
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- WithTop.somestatement and proof · cited by 1,128
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.IsStoppingTime.measurableSet_geproof · cited by 3
- MeasureTheory.IsStoppingTime.measurableSet_lt_leproof · cited by 0