Theorems · Theorem · probability

ProbabilityTheory.variance_dual_stdGaussian

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  [inst_3 : MeasurableSpace E] [BorelSpace E] (L : StrongDual ℝ E),
  ProbabilityTheory.variance (⇑L) (ProbabilityTheory.stdGaussian E) = ‖L‖ ^ 2

Defined in: Mathlib.Probability.Distributions.Gaussian.Multivariate
Cited by: 1 results in Mathlib
Foundations: Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace

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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
MeasureTheory.Measureproof · cited by 10,939
Norm.normstatement and proof · cited by 5,413
Finset.sumproof · cited by 5,195
mul_oneproof · cited by 3,885
InnerProductSpacestatement and proof · cited by 3,523
Finset.univproof · cited by 3,473
Finset.sum_congrproof · cited by 2,323

Cited by1

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ProbabilityTheory.charFunDual_stdGaussianproof · cited by 1