Theorems · Theorem · probability
ProbabilityTheory.analyticOnNhd_complexMGF
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AnalyticOnNhd ℂ (ProbabilityTheory.complexMGF X μ) {z | z.re ∈ interior (ProbabilityTheory.integrableExpSet X μ)}- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.ofPredstatement · cited by 6,101
- Complexstatement · cited by 5,565
- Complex.restatement · cited by 882
- interiorstatement · cited by 714
- AnalyticOnNhdstatement · cited by 206
- IsOpen.preimageproof · cited by 147
- isOpen_interiorproof · cited by 130
- ProbabilityTheory.integrableExpSetstatement · cited by 66
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.analyticAt_complexMGFproof · cited by 1
- ProbabilityTheory.eqOn_complexMGF_of_mgf'proof · cited by 1
- ProbabilityTheory.analyticOn_complexMGFproof · cited by 0