Theorems · Theorem · probability
MeasureTheory.Submartingale.integrable_stoppedValue
∀ {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} [inst_2 : LE E] {f : ℕ → Ω → E},
MeasureTheory.Submartingale f 𝒢 μ →
∀ {τ : Ω → ℕ∞},
MeasureTheory.IsStoppingTime 𝒢 τ →
∀ {N : ℕ}, (∀ (ω : Ω), τ ω ≤ ↑N) → MeasureTheory.Integrable (MeasureTheory.stoppedValue f τ) μ- Defined in
- Mathlib.Probability.Martingale.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- ENatstatement and proof · cited by 4,985
- MeasureTheory.Integrablestatement · cited by 1,367
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.IsStoppingTimestatement and proof · cited by 122
- MeasureTheory.Submartingalestatement and proof · cited by 63
- MeasureTheory.stoppedValuestatement · cited by 51
- MeasureTheory.Submartingale.integrableproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.expected_stoppedValue_monoproof · cited by 3
- MeasureTheory.Submartingale.stoppedProcessproof · cited by 1
- MeasureTheory.smul_le_stoppedValue_hittingBtwnproof · cited by 1
- MeasureTheory.maximal_ineqproof · cited by 0