Theorems · Theorem · probability
ProbabilityTheory.differentiableOn_complexMGF
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
DifferentiableOn ℂ (ProbabilityTheory.complexMGF X μ) {z | z.re ∈ interior (ProbabilityTheory.integrableExpSet X μ)}complexMGF X μ is holomorphic on the vertical strip
{z | z.re ∈ interior (integrableExpSet X μ)}.
- Defined in
- Mathlib.Probability.Moments.ComplexMGF
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Set.ofPredstatement and proof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- Complex.restatement and proof · cited by 882
- interiorstatement and proof · cited by 714
- Complex.expproof · cited by 612
- HasDerivAtproof · cited by 493
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.analyticOnNhd_complexMGFproof · cited by 3