Theorems · Theorem · probability
ProbabilityTheory.covariance_smul_left
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω} (c : ℝ),
ProbabilityTheory.covariance (c • X) Y μ = c * ProbabilityTheory.covariance X Y μ- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 255 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.integralproof · cited by 1,779
- mul_subproof · cited by 201
- ProbabilityTheory.covariancestatement · cited by 96
- MeasureTheory.integral_const_mulproof · cited by 45
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covariance_const_mul_leftproof · cited by 8
- ProbabilityTheory.covariance_smul_rightproof · cited by 3
- ProbabilityTheory.covariance_neg_leftproof · cited by 2