Theorems · Theorem · probability
MeasureTheory.Submartingale.stoppedAbove
∀ {Ω : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ℱ : MeasureTheory.Filtration ℕ m0}
{f : ℕ → Ω → ℝ} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.Submartingale f ℱ μ → ∀ (r : ℝ), MeasureTheory.Submartingale (MeasureTheory.stoppedAbove f r) ℱ μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.Submartingalestatement and proof · cited by 63
- MeasureTheory.Submartingale.stronglyAdaptedproof · cited by 14
- MeasureTheory.stoppedAbovestatement · cited by 5
- MeasureTheory.Submartingale.stoppedProcessproof · cited by 1
- MeasureTheory.StronglyAdapted.isStoppingTime_leastGEproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.exists_tendsto_of_abs_bddAbove_auxproof · cited by 1
- MeasureTheory.Submartingale.eLpNorm_stoppedAbove_leproof · cited by 1