Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.min_const

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

Defined in: Mathlib.Probability.Process.Stopping
Cited by: 8 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder

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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
WithTopstatement and proof · cited by 3,754
WithTop.somestatement · cited by 1,128
MeasureTheory.Filtrationstatement and proof · cited by 425
MeasureTheory.IsStoppingTimestatement and proof · cited by 122
MeasureTheory.IsStoppingTime.minproof · cited by 12
MeasureTheory.isStoppingTime_constproof · cited by 12

Cited by8

Results whose statement or proof uses this declaration.

MeasureTheory.IsStoppingTime.measurableSet_le_stopping_timeproof · cited by 4
MeasureTheory.IsStoppingTime.measurableSpace_min_conststatement · cited by 2
MeasureTheory.measurable_stoppedValueproof · cited by 2
MeasureTheory.measurableSet_preimage_stoppedValue_interproof · cited by 1
MeasureTheory.IsStoppingTime.measurableSet_inter_leproof · cited by 1
MeasureTheory.IsStoppingTime.measurableSet_inter_le_const_iffstatement · cited by 1
MeasureTheory.IsStoppingTime.measurableSet_min_const_iffstatement · cited by 0
MeasureTheory.condExp_min_stopping_time_ae_eq_restrict_le_conststatement and proof · cited by 0