Theorems · Theorem · probability
ProbabilityTheory.covariance_sub_sub
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y Z T : Ω → ℝ} {μ : MeasureTheory.Measure Ω}
[MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ →
MeasureTheory.MemLp Y 2 μ →
MeasureTheory.MemLp Z 2 μ →
MeasureTheory.MemLp T 2 μ →
ProbabilityTheory.covariance (X - Y) (Z - T) μ =
ProbabilityTheory.covariance X Z μ - ProbabilityTheory.covariance X T μ -
ProbabilityTheory.covariance Y Z μ +
ProbabilityTheory.covariance Y T μ- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.MemLpstatement and proof · cited by 457
- ProbabilityTheory.covariancestatement and proof · cited by 96
- MeasureTheory.MemLp.subproof · cited by 17
- ProbabilityTheory.covariance_sub_leftproof · cited by 2
- ProbabilityTheory.covariance_sub_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covariance_fun_sub_fun_subproof · cited by 1