Theorems · Theorem · probability
MeasureTheory.IsStronglyPredictable.predictablePart_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 : ℕ → Ω → E} {ℱ : MeasureTheory.Filtration ℕ m0}
[MeasureTheory.SigmaFiniteFiltration μ ℱ],
MeasureTheory.IsStronglyPredictable ℱ f →
(∀ (n : ℕ), MeasureTheory.Integrable (f n) μ) → ∀ (n : ℕ), MeasureTheory.predictablePart f ℱ μ n =ᵐ[μ] f n - f 0- Defined in
- Mathlib.Probability.Martingale.Centering
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Finset.sumproof · cited by 5,195
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- Finset.rangeproof · cited by 1,341
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.condExpproof · cited by 234
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.IsPredictable.martingalePart_eqproof · cited by 0