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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
Assumes
PreorderNormedAddCommGroupNormedSpaceLE

Around this declaration

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

MeasureTheory.Submartingale.stronglyMeasurable · cited by 7Submartingale.stronglyMea…MeasureTheory.Submartingale.condExp_sub_nonneg · cited by 3Submartingale.condExp_sub…MeasureTheory.Submartingale.sum_upcrossingStrat_mul · cited by 2Submartingale.sum_upcross…MeasureTheory.Submartingale.stoppedAbove · cited by 2Submartingale.stoppedAboveMeasureTheory.Submartingale.sum_smul_sub · cited by 2Submartingale.sum_smul_subMeasureTheory.Submartingale.upcrossings_ae_lt_top' · cited by 1Submartingale.upcrossings…MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part · cited by 1Submartingale.mul_lintegr…MeasureTheory.Submartingale.stoppedProcess · cited by 1Submartingale.stoppedProc…MeasureTheory.smul_le_stoppedValue_hittingBtwn · cited by 1MeasureTheory.smul_le_sto…MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto · cited by 1Submartingale.bddAbove_if…MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul · cited by 1Submartingale.sum_sub_upc…MeasureTheory.Submartingale.sup · cited by 1Submartingale.supMeasureTheory.maximal_ineq · cited by 0MeasureTheory.maximal_ineqMeasureTheory.submartingale_iff_condExp_sub_nonneg · cited by 0MeasureTheory.submartinga…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasurePreorder · cited by 7952PreorderMeasureTheory.Filtration · cited by 425MeasureTheory.FiltrationMeasureTheory.StronglyAdapted · cited by 81MeasureTheory.StronglyAda…MeasureTheory.Submartingale · cited by 63MeasureTheory.Submartinga…Submartingale.stronglyAdaptedCITED BYCITES

Cites9

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Cited by14

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