Theorems · Theorem · probability
ProbabilityTheory.analyticAt_mgf
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {t : ℝ},
t ∈ interior (ProbabilityTheory.integrableExpSet X μ) → AnalyticAt ℝ (ProbabilityTheory.mgf X μ) tThe moment-generating function is analytic at every t ∈ interior (integrableExpSet X μ).
- Defined in
- Mathlib.Probability.Moments.MGFAnalytic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 289 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
- interiorstatement and proof · cited by 714
- AnalyticAtstatement and proof · cited by 321
- ProbabilityTheory.mgfstatement · cited by 113
- ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
- AnalyticAt.re_ofRealproof · cited by 2
- ProbabilityTheory.re_complexMGF_ofReal'proof · cited by 1
- ProbabilityTheory.analyticAt_complexMGFproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.differentiableAt_mgfproof · cited by 3
- ProbabilityTheory.analyticOnNhd_mgfproof · cited by 2
- ProbabilityTheory.analyticAt_cgfproof · cited by 2
- ProbabilityTheory.hasFPowerSeriesAt_mgfproof · cited by 0