Theorems · Theorem · probability
ProbabilityTheory.mgf_add_measure
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {t : ℝ}
{ν : MeasureTheory.Measure Ω},
MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ →
MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) ν →
ProbabilityTheory.mgf X (μ + ν) t = ProbabilityTheory.mgf X μ t + ProbabilityTheory.mgf X ν t- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- Real.expstatement and proof · cited by 871
- ProbabilityTheory.mgfstatement and proof · cited by 113
- MeasureTheory.integral_add_measureproof · cited by 9
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