Theorems · Theorem · probability
ProbabilityTheory.differentiableAt_iteratedDeriv_mgf
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {v : ℝ},
v ∈ interior (ProbabilityTheory.integrableExpSet X μ) →
∀ (n : ℕ), DifferentiableAt ℝ (iteratedDeriv n (ProbabilityTheory.mgf X μ)) v- 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.
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
- DifferentiableAtstatement · cited by 617
- iteratedDerivstatement · cited by 188
- ProbabilityTheory.mgfstatement · cited by 113
- ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
- AnalyticAt.differentiableAtproof · cited by 18
- ProbabilityTheory.analyticAt_iteratedDeriv_mgfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iteratedDeriv_two_cgfproof · cited by 1