Theorems · Definition · probability
ProbabilityTheory.covariance
{Ω : Type u_1} → {mΩ : MeasurableSpace Ω} → (Ω → ℝ) → (Ω → ℝ) → MeasureTheory.Measure Ω → ℝThe covariance of two real-valued random variables defined as
the integral of (X - 𝔼[X])(Y - 𝔼[Y]).
- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 250 from the axioms, rests on 6,485 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MeasureTheory.integralproof · cited by 1,779
Cited by96
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covariance_selfstatement · cited by 11
- ProbabilityTheory.covariance_const_mul_leftstatement · cited by 8
- ProbabilityTheory.covariance_const_mul_rightstatement · cited by 8
- ProbabilityTheory.covariance_commstatement · cited by 6
- ProbabilityTheory.variance_addstatement and proof · cited by 5
- ProbabilityTheory.IsPreBrownianReal.covariance_evalstatement and proof · cited by 5
- ProbabilityTheory.covarianceBilin_apply_eq_covstatement and proof · cited by 5
- ProbabilityTheory.covariance_mapstatement · cited by 5
- ProbabilityTheory.covariance_sum_left'statement and proof · cited by 5
- ProbabilityTheory.IndepFun.covariance_eq_zerostatement · cited by 4
- ProbabilityTheory.BrownianReal.covariance_eval_projectiveFamilystatement · cited by 4
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covariancestatement and proof · cited by 4