Theorems · Theorem · probability
MeasureTheory.martingale_nat
∀ {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.IsFiniteMeasure μ]
{f : ℕ → Ω → E},
MeasureTheory.StronglyAdapted 𝒢 f →
(∀ (i : ℕ), MeasureTheory.Integrable (f i) μ) →
(∀ (i : ℕ), f i =ᵐ[μ] μ[f (i + 1) | ↑𝒢 i]) → MeasureTheory.Martingale f 𝒢 μ- Defined in
- Mathlib.Probability.Martingale.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.martingale_of_condExp_sub_eq_zero_natproof · cited by 0
- MeasureTheory.martingale_of_setIntegral_eq_succproof · cited by 0