Theorems · Theorem · probability
ProbabilityTheory.IndepFun.covariance_eq_zero
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
ProbabilityTheory.IndepFun X Y μ →
MeasureTheory.MemLp X 2 μ → MeasureTheory.MemLp Y 2 μ → ProbabilityTheory.covariance X Y μ = 0- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 271 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Filter.Eventuallyproof · cited by 3,134
- MeasureTheory.aeproof · cited by 2,352
- MeasureTheory.integralproof · cited by 1,779
- Filter.univ_mem'proof · cited by 1,672
- MulZeroClass.zero_mulproof · cited by 1,625
- Filter.mp_memproof · cited by 1,537
- sub_selfproof · cited by 996
- MeasureTheory.MemLpstatement and proof · cited by 457
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun.variance_addproof · cited by 2
- ProbabilityTheory.IndepFun.variance_sumproof · cited by 2
- ProbabilityTheory.HasIndepIncrements.isPreBrownianReal_of_hasLawproof · cited by 1
- ProbabilityTheory.covariance_fst_snd_prodproof · cited by 0