Theorems · Theorem · probability
ProbabilityTheory.variance_add
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ →
MeasureTheory.MemLp Y 2 μ →
ProbabilityTheory.variance (X + Y) μ =
ProbabilityTheory.variance X μ + 2 * ProbabilityTheory.covariance X Y μ + ProbabilityTheory.variance Y μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 5 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.
Cites15
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
- ENNRealstatement · cited by 9,879
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.MemLpstatement and proof · cited by 457
- ProbabilityTheory.variancestatement and proof · cited by 104
- ProbabilityTheory.covariancestatement and proof · cited by 96
- MeasureTheory.MemLp.addproof · cited by 24
- ProbabilityTheory.covariance_selfproof · cited by 11
- MeasureTheory.MemLp.aemeasurableproof · cited by 10
- AEMeasurable.addproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_strongDualproof · cited by 3
- ProbabilityTheory.variance_subproof · cited by 2
- ProbabilityTheory.IndepFun.variance_addproof · cited by 2
- ProbabilityTheory.variance_fun_addproof · cited by 0