Theorems · Theorem · probability
MeasureTheory.Martingale.supermartingale
∀ {Ω : Type u_1} {E : Type u_2} {ι : Type u_3} [inst : Preorder ι] {m0 : MeasurableSpace Ω}
{μ : MeasureTheory.Measure Ω} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] {f : ι → Ω → E}
{ℱ : MeasureTheory.Filtration ι m0} [CompleteSpace E] [inst_4 : Preorder E],
MeasureTheory.Martingale f ℱ μ → MeasureTheory.Supermartingale f ℱ μ- Defined in
- Mathlib.Probability.Martingale.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Preorderstatement and proof · cited by 7,952
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.Filtrationstatement and proof · cited by 425
- Filter.EventuallyEq.leproof · cited by 46
- MeasureTheory.Martingalestatement and proof · cited by 46
- MeasureTheory.Supermartingalestatement · cited by 23
- MeasureTheory.Martingale.integrableproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.sub_martingaleproof · cited by 3
- MeasureTheory.Supermartingale.add_martingaleproof · cited by 0
- MeasureTheory.martingale_iffproof · cited by 0