Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet_inter_le

∀ {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 → MeasurableSet (s ∩ {ω | τ ω ≤ π ω})

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 1 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace SecondCountableTopology OrderTopology

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Cites21

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
Set.extproof · cited by 2,266
OrderTopologystatement and proof · cited by 1,355
WithTop.someproof · cited by 1,128
SecondCountableTopologystatement and proof · cited by 750
MeasureTheory.Filtrationstatement and proof · cited by 425

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.measurableSet_inter_le_iffproof · cited by 3