Theorems · Theorem · probability
ProbabilityTheory.analyticOn_mgf
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AnalyticOn ℝ (ProbabilityTheory.mgf X μ) (interior (ProbabilityTheory.integrableExpSet X μ))The moment-generating function is analytic on the interior of the interval on which it is defined.
- Defined in
- Mathlib.Probability.Moments.MGFAnalytic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- interiorstatement · cited by 714
- AnalyticOnstatement · cited by 161
- ProbabilityTheory.mgfstatement · cited by 113
- ProbabilityTheory.integrableExpSetstatement · cited by 66
- AnalyticOnNhd.analyticOnproof · cited by 23
- ProbabilityTheory.analyticOnNhd_mgfproof · cited by 2
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