Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet_le_stopping_time

∀ {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), MeasureTheory.IsStoppingTime f π → MeasurableSet {ω | τ ω ≤ π ω}

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 4 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace SecondCountableTopology OrderTopology

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Cites22

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
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 by4

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
MeasureTheory.Martingale.condExp_stoppedValue_stopping_time_ae_eq_restrict_leproof · cited by 1
MeasureTheory.Martingale.stoppedValue_min_ae_eq_condExpproof · cited by 0