Theorems · Theorem · probability
ProbabilityTheory.analyticOn_complexMGF
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AnalyticOn ℂ (ProbabilityTheory.complexMGF X μ) {z | z.re ∈ interior (ProbabilityTheory.integrableExpSet X μ)}complexMGF X μ is analytic on the vertical strip
{z | z.re ∈ interior (integrableExpSet X μ)}.
- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- AnalyticOnstatement · cited by 161
- ProbabilityTheory.integrableExpSetstatement · cited by 66
- ProbabilityTheory.complexMGFstatement · cited by 23
- AnalyticOnNhd.analyticOnproof · cited by 23
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