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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) → Prop

A 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
Assumes
TopologicalSpacePreorderOrderBot

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.IsStronglyPredictable.measurable_add_one · cited by 6IsStronglyPredictable.mea…MeasureTheory.IsStronglyPredictable.of_measurable_add_one · cited by 4IsStronglyPredictable.of_…MeasureTheory.IsStronglyPredictable.stronglyAdapted · cited by 3IsStronglyPredictable.str…MeasureTheory.IsStronglyPredictable.isStronglyProgressive · cited by 3IsStronglyPredictable.isS…MeasureTheory.IsStronglyPredictable.predictablePart_eq · cited by 1IsStronglyPredictable.pre…MeasureTheory.martingalePart_add_ae_eq · cited by 1MeasureTheory.martingaleP…MeasureTheory.IsStronglyPredictable.iff_measurable_add_one · cited by 1IsStronglyPredictable.iff…MeasureTheory.Martingale.eq_zero_of_predictable' · cited by 0Martingale.eq_zero_of_pre…MeasureTheory.IsPredictable.martingalePart_eq · cited by 0IsPredictable.martingaleP…MeasureTheory.Submartingale.zero_le_of_predictable' · cited by 0Submartingale.zero_le_of_…MeasureTheory.IsPredictable.measurable_add_one · cited by 0IsPredictable.measurable_…MeasureTheory.IsPredictable · cited by 0MeasureTheory.IsPredictab…MeasureTheory.IsPredictable.of_measurable_add_one · cited by 0IsPredictable.of_measurab…MeasureTheory.Supermartingale.le_zero_of_predictable' · cited by 0Supermartingale.le_zero_o…MeasureTheory.IsPredictable.progMeasurable · cited by 0IsPredictable.progMeasura…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpacePreorder · cited by 7952PreorderOrderBot · cited by 1055OrderBotMeasureTheory.Filtration · cited by 425MeasureTheory.FiltrationMeasureTheory.StronglyMeasurable · cited by 363MeasureTheory.StronglyMea…MeasureTheory.IsStronglyPredi…CITED BYCITES

Cites6

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Cited by18

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