Theorems · Theorem · measure theory
MeasureTheory.charFun_eq_charFunDual_toDualMap
∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] {mE : MeasurableSpace E}
{μ : MeasureTheory.Measure E} (t : E),
MeasureTheory.charFun μ t = MeasureTheory.charFunDual μ ((InnerProductSpace.toDualMap ℝ E) t)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 251 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.
- DFunLike.coestatement · 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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- Inner.innerproof · cited by 1,089
- Complex.Iproof · cited by 866
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.charFun_map_finsetSum_eq_prodproof · cited by 3
- ProbabilityTheory.IsGaussian.charFun_eqproof · cited by 2
- ProbabilityTheory.isGaussian_iff_charFun_eqproof · cited by 1
- MeasureTheory.charFun_toDual_symm_eq_charFunDualproof · cited by 0
- ProbabilityTheory.isGaussian_iff_gaussian_charFunproof · cited by 0
- ProbabilityTheory.charFun_map_sum_pi_eq_prodproof · cited by 0