Theorems · Theorem · probability
MeasureTheory.StronglyAdapted.neg
∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : Preorder ι] {f : MeasureTheory.Filtration ι m}
{β : ι → Type u_3} [inst_1 : (i : ι) → TopologicalSpace (β i)] {u : (i : ι) → Ω → β i}
[inst_2 : (i : ι) → AddGroup (β i)] [∀ (i : ι), ContinuousNeg (β i)],
MeasureTheory.StronglyAdapted f u → MeasureTheory.StronglyAdapted f (-u)- Defined in
- Mathlib.Probability.Process.Adapted
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Preorderstatement and proof · cited by 7,952
- AddGroupstatement and proof · cited by 4,410
- MeasureTheory.Filtrationstatement and proof · cited by 425
- ContinuousNegstatement and proof · cited by 119
- MeasureTheory.StronglyAdaptedstatement and proof · cited by 81
- MeasureTheory.StronglyMeasurable.negproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.negproof · cited by 7
- MeasureTheory.Supermartingale.negproof · cited by 3
- MeasureTheory.Martingale.negproof · cited by 2
- MeasureTheory.supermartingale_natproof · cited by 0
- MeasureTheory.supermartingale_of_condExp_sub_nonneg_natproof · cited by 0
- MeasureTheory.supermartingale_of_setIntegral_succ_leproof · cited by 0