Theorems · Theorem · probability
ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
{μ : MeasureTheory.Measure E} [ProbabilityTheory.IsGaussian μ] [CompleteSpace E] [SecondCountableTopology E],
∫ (x : E), id x ∂μ = 0 →
∀ (L : StrongDual ℝ E), MeasureTheory.charFunDual μ L = Complex.exp (-↑(ProbabilityTheory.variance (⇑L) μ) / 2)Characteristic function of a centered Gaussian measure.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement · cited by 5,565
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.integralstatement and proof · cited by 1,779
- Complex.ofRealstatement · cited by 1,654
- map_zeroproof · cited by 1,614
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.