Theorems · Theorem · probability

ProbabilityTheory.integrable_rpow_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) →
    ∀ {p : ℝ}, 0 ≤ p → MeasureTheory.Integrable (fun ω => ↑(X ω ^ p) * Complex.exp (z * ↑(X ω))) μ

Defined in: Mathlib.Probability.Moments.IntegrableExpMul
Cited by: 1 results in Mathlib
Foundations: Depth 213 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
Complexstatement and proof · cited by 5,565
MulZeroClass.mul_zeroproof · cited by 2,091
absproof · cited by 1,814
Complex.ofRealstatement and proof · cited by 1,654
MeasureTheory.Integrablestatement and proof · cited by 1,367
le_of_ltproof · cited by 1,175
sub_zeroproof · cited by 938
Complex.restatement and proof · cited by 882

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ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSetproof · cited by 2