Theorems · Theorem · measure theory
MeasureTheory.condExp_smul_of_aestronglyMeasurable_left
∀ {Ω : Type u_1} {m mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {E : Type u_2} [inst : NormedAddCommGroup E]
[inst_1 : NormedSpace ℝ E] [CompleteSpace E] {f : Ω → ℝ} {g : Ω → E},
MeasureTheory.AEStronglyMeasurable f μ →
MeasureTheory.Integrable (f • g) μ → MeasureTheory.Integrable g μ → μ[f • g | m] =ᵐ[μ] f • μ[g | m]Pull-out property of the conditional expectation.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 305 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
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.condExpstatement · cited by 234
- ContinuousLinearMap.lsmulproof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.sum_smul_subproof · cited by 2