Theorems · Theorem · probability
ProbabilityTheory.complexMGF_id_map
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AEMeasurable X μ → ProbabilityTheory.complexMGF id (MeasureTheory.Measure.map X μ) = ProbabilityTheory.complexMGF X μ- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 255 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- AEMeasurablestatement and proof · cited by 840
- Complex.expproof · cited by 612
- continuous_id'proof · cited by 295
- Complex.continuous_ofRealproof · cited by 107
- Continuous.comp_aestronglyMeasurableproof · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.complexMGF_congr_identDistribproof · cited by 0
- ProbabilityTheory.complexMGF_gaussianRealproof · cited by 0
- ProbabilityTheory.complexMGF_mul_Iproof · cited by 0