Theorems · Definition · probability
ProbabilityTheory.covarianceBilin
{E : Type u_1} →
[inst : NormedAddCommGroup E] →
[inst_1 : InnerProductSpace ℝ E] →
[inst_2 : MeasurableSpace E] → [BorelSpace E] → MeasureTheory.Measure E → E →L[ℝ] E →L[ℝ] ℝCovariance of a measure on an inner product space, as a continuous bilinear form.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- BorelSpacestatement and proof · cited by 1,602
- LinearIsometry.toContinuousLinearMapproof · cited by 47
- InnerProductSpace.toDualMapproof · cited by 26
- ProbabilityTheory.covarianceBilinDualproof · cited by 22
- ContinuousLinearMap.bilinearCompproof · cited by 11
Cited by25
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceBilin_apply_eq_covstatement · cited by 5
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
- ProbabilityTheory.IsGaussian.extstatement and proof · cited by 3
- ProbabilityTheory.covarianceBilin_eq_covarianceBilinDualstatement · cited by 3
- ProbabilityTheory.covarianceBilin_multivariateGaussianstatement and proof · cited by 3
- ProbabilityTheory.covarianceBilin_of_not_memLpstatement · cited by 2
- ProbabilityTheory.IsGaussian.charFun_eq'statement and proof · cited by 2
- ProbabilityTheory.covarianceBilin_applystatement · cited by 2
- ProbabilityTheory.covarianceBilin_realstatement · cited by 1
- ProbabilityTheory.covarianceBilin_selfstatement · cited by 1
- ProbabilityTheory.covarianceBilin_self_nonnegstatement · cited by 1
- ProbabilityTheory.covarianceBilin_stdGaussianstatement · cited by 1