Theorems · Theorem · probability

ProbabilityTheory.charFun_stdGaussian

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  [inst_3 : MeasurableSpace E] [BorelSpace E] (t : E),
  MeasureTheory.charFun (ProbabilityTheory.stdGaussian E) t = Complex.exp (-↑‖t‖ ^ 2 / 2)

Defined in: Mathlib.Probability.Distributions.Gaussian.Multivariate
Cited by: 2 results in Mathlib
Foundations: Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace

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Cites56

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measureproof · cited by 10,939
Complexstatement and proof · cited by 5,565
Norm.normstatement and proof · cited by 5,413
InnerProductSpacestatement and proof · cited by 3,523
Finset.univproof · cited by 3,473
one_mulproof · cited by 2,841
Finset.sum_congrproof · cited by 2,323
mul_commproof · cited by 2,262

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.covarianceBilin_stdGaussianproof · cited by 1
ProbabilityTheory.map_pi_eq_stdGaussianproof · cited by 1