Theorems · Theorem · probability

ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul

∀ {Ω : Type u_1} {Ω' : Type u_2} {mΩ : MeasurableSpace Ω} {mΩ' : MeasurableSpace Ω'} {X : Ω → ℝ} {c : NNReal}
  {κ : ProbabilityTheory.Kernel Ω' Ω}
  {ν : autoParam (MeasureTheory.Measure Ω') ProbabilityTheory.Kernel.HasSubgaussianMGF._auto_1},
  ProbabilityTheory.Kernel.HasSubgaussianMGF X c κ ν →
    ∀ (t : ℝ), MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) (ν.bind ⇑κ)

Defined in

Mathlib.Probability.Moments.SubGaussian

Cited by

11 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound