Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.min

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : LinearOrder ι] {f : MeasureTheory.Filtration ι m}
  {τ π : Ω → WithTop ι},
  MeasureTheory.IsStoppingTime f τ →
    MeasureTheory.IsStoppingTime f π → MeasureTheory.IsStoppingTime f fun ω => min (τ ω) (π ω)

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 12 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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

MeasurableSpacestatement and proof · cited by 13,106
LinearOrderstatement and proof · cited by 8,572
Set.ofPredproof · cited by 6,101
WithTopstatement and proof · cited by 3,754
MeasurableSetproof · cited by 3,075
MeasureTheory.Filtrationstatement and proof · cited by 425
MeasureTheory.IsStoppingTimestatement and proof · cited by 122
MeasurableSet.unionproof · cited by 55

Cited by12

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.min_constproof · cited by 8
MeasureTheory.IsStoppingTime.measurableSet_min_iffstatement · cited by 5
MeasureTheory.IsStoppingTime.measurableSpace_minstatement and proof · cited by 4
MeasureTheory.IsStoppingTime.measurableSet_inter_le_iffstatement · cited by 3
MeasureTheory.IsStoppingTime.measurableSet_stopping_time_le_minstatement · cited by 2
MeasureTheory.IsStoppingTime.measurableSet_eq_stopping_time_minstatement and proof · cited by 1
MeasureTheory.Submartingale.stoppedProcessproof · cited by 1
MeasureTheory.condExp_min_stopping_time_ae_eq_restrict_lestatement and proof · cited by 1
MeasureTheory.IsStoppingTime.measurableSet_inter_lestatement and proof · cited by 1
ProbabilityTheory.IsLocalizingSequence.isPrelocalizingSequence_inf_extractionproof · cited by 1
ProbabilityTheory.IsLocalizingSequence.minproof · cited by 1
MeasureTheory.Martingale.stoppedValue_min_ae_eq_condExpstatement and proof · cited by 0