Theorems · Theorem · probability
ProbabilityTheory.mgf_pos
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {t : ℝ}
[MeasureTheory.IsProbabilityMeasure μ],
MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ → 0 < ProbabilityTheory.mgf X μ t- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Integrablestatement and proof · cited by 1,367
- Real.expstatement and proof · cited by 871
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- ProbabilityTheory.mgfstatement · cited by 113
- MeasureTheory.IsProbabilityMeasure.ne_zeroproof · cited by 17
- ProbabilityTheory.mgf_pos'proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.cgf_sum₀proof · cited by 1
- ProbabilityTheory.integrableExpSet_eq_of_mgfproof · cited by 0
- ProbabilityTheory.eqOn_complexMGF_of_mgfproof · cited by 0