Theorems · Theorem · probability

ProbabilityTheory.analyticAt_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), AnalyticAt ℝ (iteratedDeriv n (ProbabilityTheory.mgf X μ)) v

Defined in: Mathlib.Probability.Moments.MGFAnalytic
Cited by: 1 results in Mathlib
Foundations: Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound

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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 · cited by 321
iteratedDerivstatement · cited by 188
ProbabilityTheory.mgfstatement · cited by 113
ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgfproof · cited by 2

Cited by1

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ProbabilityTheory.differentiableAt_iteratedDeriv_mgfproof · cited by 1