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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] ℝ

Covariance of a measure on an inner product space, as a continuous bilinear form.

Defined in
Mathlib.Probability.Moments.CovarianceBilin
Cited by
25 results in Mathlib
Foundations
Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupInnerProductSpaceMeasurableSpaceBorelSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.covarianceBilin_apply_eq_cov · cited by 5ProbabilityTheory.covaria…ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covariance · cited by 4IsGaussianProcess.isPreBr…ProbabilityTheory.IsGaussian.ext · cited by 3IsGaussian.extProbabilityTheory.covarianceBilin_eq_covarianceBilinDual · cited by 3ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_multivariateGaussian · cited by 3ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_of_not_memLp · cited by 2ProbabilityTheory.covaria…ProbabilityTheory.IsGaussian.charFun_eq' · cited by 2IsGaussian.charFun_eq'ProbabilityTheory.covarianceBilin_apply · cited by 2ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_real · cited by 1ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_self · cited by 1ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_self_nonneg · cited by 1ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin_stdGaussian · cited by 1ProbabilityTheory.covaria…ProbabilityTheory.covarianceBilin.congr_simp · cited by 1covarianceBilin.congr_simpProbabilityTheory.measurePreserving_restrict₂_multivariateGaussian · cited by 1ProbabilityTheory.measure…ProbabilityTheory.isPosSemidef_covarianceBilin · cited by 1ProbabilityTheory.isPosSe…Real · cited by 25697RealRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureContinuousLinearMap · cited by 5352ContinuousLinearMapInnerProductSpace · cited by 3523InnerProductSpaceBorelSpace · cited by 1602BorelSpaceLinearIsometry.toContinuousLinearMap · cited by 47LinearIsometry.toContinuo…InnerProductSpace.toDualMap · cited by 26InnerProductSpace.toDualM…ProbabilityTheory.covarianceBilinDual · cited by 22ProbabilityTheory.covaria…ContinuousLinearMap.bilinearComp · cited by 11ContinuousLinearMap.bilin…ProbabilityTheory.covarianceB…CITED BYCITES

Cites12

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Cited by25

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