Theorems · Theorem · probability

MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le

∀ {Ω : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ℱ : MeasureTheory.Filtration ℕ m0}
  {f : ℕ → Ω → ℝ} {r : ℝ} {R : NNReal} [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.Submartingale f ℱ μ →
    0 ≤ r →
      f 0 = 0 →
        (∀ᵐ (ω : Ω) ∂μ, ∀ (i : ℕ), |f (i + 1) ω - f i ω| ≤ ↑R) →
          ∀ (i : ℕ),
            MeasureTheory.eLpNorm (MeasureTheory.stoppedAbove f r i) 1 μ ≤ 2 * μ Set.univ * ENNReal.ofReal (r + ↑R)

Defined in: Mathlib.Probability.Martingale.BorelCantelli
Cited by: 1 results in Mathlib
Foundations: Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure

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DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
NNRealstatement and proof · cited by 4,310
Set.univstatement · cited by 3,945
Filter.Eventuallystatement and proof · cited by 3,134
MeasureTheory.aestatement and proof · cited by 2,352
absstatement and proof · cited by 1,814
MeasureTheory.integralproof · cited by 1,779

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MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le'proof · cited by 1