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Theorems · Definition · measure theory

MeasureTheory.charFun

{E : Type u_2} → {mE : MeasurableSpace E} → [Inner ℝ E] → MeasureTheory.Measure E → E → ℂ

The characteristic function of a measure in an inner product space.

Defined in
Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic
Cited by
84 results in Mathlib
Foundations
Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Inner

Around this declaration

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

ProbabilityTheory.IsGaussian.charFunDual_eq · cited by 9IsGaussian.charFunDual_eqMeasureTheory.charFun_apply · cited by 7MeasureTheory.charFun_app…MeasureTheory.Measure.ext_of_charFun · cited by 7Measure.ext_of_charFunProbabilityTheory.charFun_gaussianReal · cited by 7ProbabilityTheory.charFun…MeasureTheory.charFun_eq_charFunDual_toDualMap · cited by 6MeasureTheory.charFun_eq_…ProbabilityTheory.isGaussian_iff_gaussian_charFunDual · cited by 4ProbabilityTheory.isGauss…MeasureTheory.charFun_eq_fourierIntegral' · cited by 3MeasureTheory.charFun_eq_…MeasureTheory.charFun_map_eq_charFunDual_smul · cited by 3MeasureTheory.charFun_map…ProbabilityTheory.iIndepFun.charFun_map_finsetSum_eq_prod · cited by 3iIndepFun.charFun_map_fin…ProbabilityTheory.iIndepFun.charFun_map_fun_finsetSum_eq_prod · cited by 3iIndepFun.charFun_map_fun…MeasureTheory.charFun_conv · cited by 2MeasureTheory.charFun_convMeasureTheory.charFun_eq_integral_innerProbChar · cited by 2MeasureTheory.charFun_eq_…ProbabilityTheory.charFun_stdGaussian · cited by 2ProbabilityTheory.charFun…MeasureTheory.charFun_map_smul · cited by 2MeasureTheory.charFun_map…MeasureTheory.charFun_pi · cited by 2MeasureTheory.charFun_piReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureComplex · cited by 5565ComplexMeasureTheory.integral · cited by 1779MeasureTheory.integralComplex.ofReal · cited by 1654Complex.ofRealInner.inner · cited by 1089Inner.innerComplex.I · cited by 866Complex.IComplex.exp · cited by 612Complex.expInner · cited by 14InnerMeasureTheory.charFunCITED BYCITES

Cites10

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

Cited by84

Results whose statement or proof uses this declaration.