Theorems · Theorem · probability
ProbabilityTheory.IndepFun.mgf_add
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {t : ℝ} {X Y : Ω → ℝ},
ProbabilityTheory.IndepFun X Y μ →
MeasureTheory.AEStronglyMeasurable (fun ω => Real.exp (t * X ω)) μ →
MeasureTheory.AEStronglyMeasurable (fun ω => Real.exp (t * Y ω)) μ →
ProbabilityTheory.mgf (X + Y) μ t = ProbabilityTheory.mgf X μ t * ProbabilityTheory.mgf Y μ t- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.integralproof · cited by 1,779
- Real.expstatement and proof · cited by 871
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- mul_addproof · cited by 413
- ProbabilityTheory.IndepFunstatement and proof · cited by 192
- ProbabilityTheory.mgfstatement · cited by 113
- Real.exp_addproof · cited by 39
- ProbabilityTheory.IndepFun.exp_mulproof · cited by 2
- ProbabilityTheory.IndepFun.integral_mul_eq_mul_integralproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.mgf_sum₀proof · cited by 3
- ProbabilityTheory.HasSubgaussianMGF.add_of_indepFunproof · cited by 1
- ProbabilityTheory.IndepFun.mgf_add'proof · cited by 0
- ProbabilityTheory.IndepFun.cgf_addproof · cited by 0