Theorems · Definition · measure theory
MeasureTheory.charFun
{E : Type u_2} → {mE : MeasurableSpace E} → [Inner ℝ E] → MeasureTheory.Measure E → E → ℂThe characteristic function of a measure in an inner product space.
- 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.
Cites10
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement · cited by 5,565
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- Inner.innerproof · cited by 1,089
- Complex.Iproof · cited by 866
- Complex.expproof · cited by 612
- Innerstatement and proof · cited by 14
Cited by84
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussian.charFunDual_eqproof · cited by 9
- MeasureTheory.charFun_applystatement · cited by 7
- MeasureTheory.Measure.ext_of_charFunstatement and proof · cited by 7
- ProbabilityTheory.charFun_gaussianRealstatement · cited by 7
- MeasureTheory.charFun_eq_charFunDual_toDualMapstatement · cited by 6
- ProbabilityTheory.isGaussian_iff_gaussian_charFunDualproof · cited by 4
- MeasureTheory.charFun_eq_fourierIntegral'statement · cited by 3
- MeasureTheory.charFun_map_eq_charFunDual_smulstatement and proof · cited by 3
- ProbabilityTheory.iIndepFun.charFun_map_finsetSum_eq_prodstatement and proof · cited by 3
- ProbabilityTheory.iIndepFun.charFun_map_fun_finsetSum_eq_prodstatement and proof · cited by 3
- MeasureTheory.charFun_convstatement · cited by 2
- MeasureTheory.charFun_eq_integral_innerProbCharstatement · cited by 2