Theorems · Theorem · measure theory
MeasureTheory.charFun_eq_fourierIntegral
∀ {E : Type u_2} {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E} [inst : SeminormedAddCommGroup E]
[inst_1 : InnerProductSpace ℝ E] (t : E),
MeasureTheory.charFun μ t = VectorFourier.fourierIntegral Real.probChar μ (innerₗ E) 1 (-t)charFun is a Fourier integral for the inner product and the character probChar.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- Inner.innerproof · cited by 1,089
- neg_negproof · cited by 960
- Complex.Iproof · cited by 866
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.norm_charFun_leproof · cited by 2