Theorems · Theorem · probability
ProbabilityTheory.complexMGF_id_mul_I
∀ {μ : MeasureTheory.Measure ℝ} (t : ℝ), ProbabilityTheory.complexMGF id μ (↑t * Complex.I) = MeasureTheory.charFun μ t- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 2 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.
Cites17
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
- NormedAddCommGroupproof · cited by 15,752
- MeasurableSpaceproof · cited by 13,106
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealstatement and proof · cited by 1,654
- pow_oneproof · cited by 894
- Complex.Istatement and proof · cited by 866
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.charFun_gaussianRealproof · cited by 7
- ProbabilityTheory.complexMGF_mul_Iproof · cited by 0