Theorems · Theorem · probability

ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul

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

Defined in

Mathlib.Probability.Moments.SubGaussian

Cited by

4 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound