Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet_inter_eq_iff

∀ {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) (i : ι),
  MeasurableSet (s ∩ {ω | τ ω = ↑i}) ↔ MeasurableSet (s ∩ {ω | τ ω = ↑i})

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 6 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Preorder

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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
MeasurableSpacestatement and proof · cited by 13,106
Preorderstatement and proof · cited by 7,952
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
WithTop.somestatement and proof · cited by 1,128
MeasureTheory.Filtrationstatement and proof · cited by 425
le_iSupproof · cited by 207
Set.inter_univproof · cited by 198
MeasureTheory.Filtration.seqstatement and proof · cited by 184

Cited by6

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.measurableSet_eq'proof · cited by 5
MeasureTheory.IsStoppingTime.measurableSet_eq_of_countable_range'proof · cited by 4
MeasureTheory.Martingale.condExp_stopping_time_ae_eq_restrict_eq_const_of_le_constproof · cited by 1
MeasureTheory.condExp_stopping_time_ae_eq_restrict_eq_of_countable_rangeproof · cited by 1
MeasureTheory.Martingale.condExp_stopping_time_ae_eq_restrict_eq_constproof · cited by 0
MeasureTheory.condExp_stopping_time_ae_eq_restrict_eqproof · cited by 0