Theorems · Theorem · probability
ProbabilityTheory.mgf_undef
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {t : ℝ},
¬MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ → ProbabilityTheory.mgf X μ t = 0- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ProbabilityTheory.mgfstatement · cited by 113
- MeasureTheory.integral_undefproof · cited by 58
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.mgf_pos_iffproof · cited by 2
- ProbabilityTheory.mgf_anti_of_nonposproof · cited by 0
- ProbabilityTheory.cgf_undefproof · cited by 0
- ProbabilityTheory.mgf_mono_of_nonnegproof · cited by 0