Theorems · Definition · probability
MeasureTheory.IsStronglyPredictable
{Ω : Type u_1} →
{ι : Type u_2} →
{m : MeasurableSpace Ω} →
{E : Type u_3} →
[TopologicalSpace E] → [inst : Preorder ι] → [OrderBot ι] → MeasureTheory.Filtration ι m → (ι → Ω → E) → PropA process is said to be predictable if it is measurable with respect to the predictable σ-algebra.
- Defined in
- Mathlib.Probability.Process.Predictable
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- OrderBotstatement and proof · cited by 1,055
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.StronglyMeasurableproof · cited by 363
Cited by18
Results whose statement or proof uses this declaration.
- MeasureTheory.IsStronglyPredictable.measurable_add_onestatement and proof · cited by 6
- MeasureTheory.IsStronglyPredictable.of_measurable_add_onestatement · cited by 4
- MeasureTheory.IsStronglyPredictable.stronglyAdaptedstatement and proof · cited by 3
- MeasureTheory.IsStronglyPredictable.isStronglyProgressivestatement and proof · cited by 3
- MeasureTheory.IsStronglyPredictable.predictablePart_eqstatement and proof · cited by 1
- MeasureTheory.martingalePart_add_ae_eqproof · cited by 1
- MeasureTheory.IsStronglyPredictable.iff_measurable_add_onestatement and proof · cited by 1
- MeasureTheory.Martingale.eq_zero_of_predictable'statement and proof · cited by 0
- MeasureTheory.IsPredictable.martingalePart_eqstatement and proof · cited by 0
- MeasureTheory.Submartingale.zero_le_of_predictable'statement and proof · cited by 0
- MeasureTheory.IsPredictable.measurable_add_onestatement · cited by 0
- MeasureTheory.IsPredictableproof · cited by 0