Theorems · Theorem · probability

ProbabilityTheory.IndepFun.integrable_exp_mul_add

∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {t : ℝ} {X Y : Ω → ℝ},
  ProbabilityTheory.IndepFun X Y μ →
    MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ →
      MeasureTheory.Integrable (fun ω => Real.exp (t * Y ω)) μ →
        MeasureTheory.Integrable (fun ω => Real.exp (t * (X + Y) ω)) μ

Defined in: Mathlib.Probability.Moments.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 212 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.

Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
MeasureTheory.Integrablestatement and proof · cited by 1,367
Real.expstatement and proof · cited by 871
mul_addproof · cited by 413
ProbabilityTheory.IndepFunstatement and proof · cited by 192
Real.exp_addproof · cited by 39
ProbabilityTheory.IndepFun.exp_mulproof · cited by 2
ProbabilityTheory.IndepFun.integrable_mulproof · cited by 1

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ProbabilityTheory.iIndepFun.integrable_exp_mul_sumproof · cited by 0