Theorems · Theorem · probability
ProbabilityTheory.covariance_add_const_right
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω}
[MeasureTheory.IsProbabilityMeasure μ],
MeasureTheory.Integrable Y μ →
∀ (c : ℝ), ProbabilityTheory.covariance X (fun ω => Y ω + c) μ = ProbabilityTheory.covariance X Y μ- Defined in
- Mathlib.Probability.Moments.Covariance
- Cited by
- 2 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.
Cites8
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.Integrablestatement and proof · cited by 1,367
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- ProbabilityTheory.covariancestatement and proof · cited by 96
- ProbabilityTheory.covariance_commproof · cited by 6
- ProbabilityTheory.covariance_add_const_leftproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covariance_const_add_rightproof · cited by 1
- ProbabilityTheory.covariance_sub_const_rightproof · cited by 0