Theorems · Theorem · probability
ProbabilityTheory.analyticAt_complexMGF
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {z : ℂ},
z.re ∈ interior (ProbabilityTheory.integrableExpSet X μ) → AnalyticAt ℂ (ProbabilityTheory.complexMGF X μ) zcomplexMGF X μ is analytic at any point z with z.re ∈ interior (integrableExpSet X μ).
- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- Complex.restatement and proof · cited by 882
- interiorstatement and proof · cited by 714
- AnalyticAtstatement · cited by 321
- ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
- ProbabilityTheory.complexMGFstatement · cited by 23
- ProbabilityTheory.analyticOnNhd_complexMGFproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.analyticAt_mgfproof · cited by 4