Theorems · Theorem · probability
MeasureTheory.Martingale.eq_zero_of_predictable
∀ {Ω : Type u_1} {E : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : NormedAddCommGroup E]
[inst_1 : NormedSpace ℝ E] {𝒢 : MeasureTheory.Filtration ℕ m0} [CompleteSpace E]
[MeasureTheory.SigmaFiniteFiltration μ 𝒢] {f : ℕ → Ω → E},
MeasureTheory.Martingale f 𝒢 μ → (MeasureTheory.StronglyAdapted 𝒢 fun n => f (n + 1)) → ∀ (n : ℕ), f n =ᵐ[μ] f 0A predictable martingale is a.e. equal to its initial state.
- Defined in
- Mathlib.Probability.Martingale.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Filtrationstatement and proof · cited by 425
- Filter.EventuallyEq.symmproof · cited by 408
- Filter.EventuallyEq.transproof · cited by 123
- Filter.EventuallyEq.reflproof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.martingalePart_add_ae_eqproof · cited by 1
- MeasureTheory.Martingale.eq_zero_of_predictable'proof · cited by 0