Theorems · Theorem · probability

ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet

∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {z : ℂ},
  z.re ∈ interior (ProbabilityTheory.integrableExpSet X μ) →
    ∀ (n : ℕ), MeasureTheory.Integrable (fun ω => ↑(X ω) ^ n * Complex.exp (z * ↑(X ω))) μ

Defined in: Mathlib.Probability.Moments.IntegrableExpMul
Cited by: 2 results in Mathlib
Foundations: Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

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
TopologicalSpaceproof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Complexstatement and proof · cited by 5,565
Complex.ofRealstatement and proof · cited by 1,654
MeasureTheory.Integrablestatement and proof · cited by 1,367
Complex.restatement and proof · cited by 882
interiorstatement and proof · cited by 714
Complex.expstatement and proof · cited by 612
ContinuousENormproof · cited by 290

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_realproof · cited by 3