Theorems · Theorem · probability
ProbabilityTheory.covarianceBilinDual_self_eq_variance
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E}
[inst_1 : NormedSpace ℝ E] [inst_2 : BorelSpace E] [CompleteSpace E] [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp id 2 μ →
∀ (L : StrongDual ℝ E), ((ProbabilityTheory.covarianceBilinDual μ) L) L = ProbabilityTheory.variance (⇑L) μ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- ContinuousLinearMapstatement · cited by 5,352
- CompleteSpacestatement and proof · cited by 2,532
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun.hasGaussianLawproof · cited by 4
- ProbabilityTheory.iIndepFun.hasGaussianLawproof · cited by 3
- ProbabilityTheory.IsGaussian.charFunDual_eq'proof · cited by 3
- ProbabilityTheory.covarianceBilin_selfproof · cited by 1
- ProbabilityTheory.gaussian_charFunDual_congrproof · cited by 1