Theorems · Theorem · probability
ProbabilityTheory.covariance_neg_right
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
ProbabilityTheory.covariance X (-Y) μ = -ProbabilityTheory.covariance X Y μ- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- one_mulproof · cited by 2,841
- one_smulproof · cited by 1,374
- neg_mulproof · cited by 654
- neg_smulproof · cited by 306
- ProbabilityTheory.covariancestatement and proof · cited by 96
- ProbabilityTheory.covariance_smul_rightproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_subproof · cited by 2
- ProbabilityTheory.covariance_sub_rightproof · cited by 2
- ProbabilityTheory.covariance_fun_neg_rightproof · cited by 1