Theorems · Theorem · probability
ProbabilityTheory.mgf_id_map
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AEMeasurable X μ → ProbabilityTheory.mgf id (MeasureTheory.Measure.map X μ) = ProbabilityTheory.mgf X μ- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
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
- MeasureTheory.Measure.mapstatement · cited by 858
- AEMeasurablestatement and proof · cited by 840
- ProbabilityTheory.mgfstatement and proof · cited by 113
- Measurable.aestronglyMeasurableproof · cited by 59
- MeasurableMul.measurable_const_mulproof · cited by 12
- Measurable.expproof · cited by 9
- ProbabilityTheory.mgf_mapproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.mgf_gaussianRealproof · cited by 3
- ProbabilityTheory.HasSubgaussianMGF.id_map_iffproof · cited by 1
- ProbabilityTheory.mgf_congr_identDistribproof · cited by 0
- ProbabilityTheory.Kernel.HasSubgaussianMGF.id_map_iffproof · cited by 0
- ProbabilityTheory.mgf_diracproof · cited by 0