Theorems · Theorem · probability
ProbabilityTheory.analyticOn_cgf
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
AnalyticOn ℝ (ProbabilityTheory.cgf X μ) (interior (ProbabilityTheory.integrableExpSet X μ))The cumulant-generating function is analytic on the interior of the interval
integrableExpSet X μ.
- Defined in
- Mathlib.Probability.Moments.MGFAnalytic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- interiorstatement · cited by 714
- AnalyticOnstatement · cited by 161
- ProbabilityTheory.integrableExpSetstatement · cited by 66
- ProbabilityTheory.cgfstatement · cited by 36
- AnalyticOnNhd.analyticOnproof · cited by 23
- ProbabilityTheory.analyticOnNhd_cgfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mulproof · cited by 1