Theorems · Theorem · probability
MeasureTheory.Submartingale.stronglyAdapted
∀ {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} [inst_3 : LE E],
MeasureTheory.Submartingale f ℱ μ → MeasureTheory.StronglyAdapted ℱ f- Defined in
- Mathlib.Probability.Martingale.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.StronglyAdaptedstatement · cited by 81
- MeasureTheory.Submartingalestatement and proof · cited by 63
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.stronglyMeasurableproof · cited by 7
- MeasureTheory.Submartingale.condExp_sub_nonnegproof · cited by 3
- MeasureTheory.Submartingale.sum_upcrossingStrat_mulproof · cited by 2
- MeasureTheory.Submartingale.stoppedAboveproof · cited by 2
- MeasureTheory.Submartingale.sum_smul_subproof · cited by 2
- MeasureTheory.Submartingale.upcrossings_ae_lt_top'proof · cited by 1
- MeasureTheory.Submartingale.stoppedProcessproof · cited by 1
- MeasureTheory.smul_le_stoppedValue_hittingBtwnproof · cited by 1
- MeasureTheory.Submartingale.bddAbove_iff_exists_tendstoproof · cited by 1
- MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mulproof · cited by 1
- MeasureTheory.Submartingale.supproof · cited by 1