Theorems · Theorem · probability
MeasureTheory.predictablePart_add_ae_eq
∀ {Ω : Type u_1} {E : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : NormedAddCommGroup E]
[inst_1 : NormedSpace ℝ E] {ℱ : MeasureTheory.Filtration ℕ m0} [CompleteSpace E]
[MeasureTheory.SigmaFiniteFiltration μ ℱ] {f g : ℕ → Ω → E},
MeasureTheory.Martingale f ℱ μ →
(MeasureTheory.StronglyAdapted ℱ fun n => g (n + 1)) →
g 0 = 0 →
(∀ (n : ℕ), MeasureTheory.Integrable (g n) μ) → ∀ (n : ℕ), MeasureTheory.predictablePart (f + g) ℱ μ n =ᵐ[μ] g n- Defined in
- Mathlib.Probability.Martingale.Centering
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.Filtrationstatement and proof · cited by 425
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