Theorems · Theorem · probability
ProbabilityTheory.covariance_comm
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} (X Y : Ω → ℝ) {μ : MeasureTheory.Measure Ω},
ProbabilityTheory.covariance X Y μ = ProbabilityTheory.covariance Y X μ- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedAddCommGroupproof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.integralproof · cited by 1,779
- ProbabilityTheory.covariancestatement · cited by 96
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_addproof · cited by 5
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
- ProbabilityTheory.covariance_sum_right'proof · cited by 4
- ProbabilityTheory.covariance_smul_rightproof · cited by 3
- ProbabilityTheory.covariance_add_rightproof · cited by 3
- ProbabilityTheory.covariance_add_const_rightproof · cited by 2