Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : Preorder ι] {f : MeasureTheory.Filtration ι m}
  {τ : Ω → WithTop ι} (hτ : MeasureTheory.IsStoppingTime f τ) (s : Set Ω),
  MeasurableSet s ↔ MeasurableSet s ∧ ∀ (i : ι), MeasurableSet (s ∩ {ω | τ ω ≤ ↑i})

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 3 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Preorder

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Cites12

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
MeasurableSpacestatement and proof · cited by 13,106
Preorderstatement and proof · cited by 7,952
Set.ofPredstatement · cited by 6,101
WithTopstatement and proof · cited by 3,754
MeasurableSetstatement · cited by 3,075
iSupstatement · cited by 2,415
WithTop.somestatement · cited by 1,128
MeasureTheory.Filtrationstatement and proof · cited by 425
MeasureTheory.Filtration.seqstatement · cited by 184
MeasureTheory.IsStoppingTimestatement and proof · cited by 122
MeasureTheory.IsStoppingTime.measurableSpacestatement · cited by 49

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.measurableSpace_constproof · cited by 4
MeasureTheory.IsStoppingTime.measurableSet_le_stopping_timeproof · cited by 4
MeasureTheory.IsStoppingTime.measurableSet_inter_le_const_iffproof · cited by 1