Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet_lt_of_countable_range

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : PartialOrder ι] {τ : Ω → WithTop ι}
  {f : MeasureTheory.Filtration ι m},
  MeasureTheory.IsStoppingTime f τ → (Set.range τ).Countable → ∀ (i : ι), MeasurableSet {ω | τ ω < ↑i}

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 2 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PartialOrder

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
PartialOrderstatement and proof · cited by 6,410
Set.ofPredstatement and proof · cited by 6,101
Set.rangestatement and proof · cited by 4,705
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
Set.Countablestatement and proof · cited by 545
MeasureTheory.Filtrationstatement and proof · cited by 425
MeasureTheory.Filtration.seqstatement · cited by 184

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.measurableSet_ge_of_countable_rangeproof · cited by 1
MeasureTheory.IsStoppingTime.measurableSet_lt_of_countableproof · cited by 0