Theorems · Theorem · probability
ProbabilityTheory.uncenteredCovarianceBilinDual_apply
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E}
[inst_1 : NormedSpace ℝ E] [inst_2 : OpensMeasurableSpace E],
MeasureTheory.MemLp id 2 μ →
∀ (L₁ L₂ : StrongDual ℝ E), ((ProbabilityTheory.uncenteredCovarianceBilinDual μ) L₁) L₂ = ∫ (x : E), L₁ x * L₂ x ∂μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- RCLikeproof · cited by 2,829
- mul_commproof · cited by 2,262
- MeasureTheory.integralstatement and proof · cited by 1,779
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceOperator_innerproof · cited by 2
- ProbabilityTheory.covarianceBilinDual_applyproof · cited by 2
- ProbabilityTheory.covarianceBilinDual_commproof · cited by 2
- ProbabilityTheory.norm_uncenteredCovarianceBilinDual_leproof · cited by 0