Theorems · Theorem · probability

ProbabilityTheory.charFunDual_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),
  MeasureTheory.charFunDual (ProbabilityTheory.stdGaussian E) L = Complex.exp (-↑‖L‖ ^ 2 / 2)

Defined in: Mathlib.Probability.Distributions.Gaussian.Multivariate
Cited by: 1 results in Mathlib
Foundations: Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites23

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
Complexstatement · cited by 5,565
Norm.normstatement and proof · cited by 5,413
InnerProductSpacestatement and proof · cited by 3,523
FiniteDimensionalstatement and proof · cited by 1,854
Complex.ofRealstatement and proof · cited by 1,654
MulZeroClass.zero_mulproof · cited by 1,625
BorelSpacestatement and proof · cited by 1,602
Complex.Iproof · cited by 866

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.stdGaussian_mapproof · cited by 1