Theorems · Theorem · probability

ProbabilityTheory.Kernel.HasSubgaussianMGF.of_rat

∀ {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},
  (∀ (t : ℝ), MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) (ν.bind ⇑κ)) →
    (∀ (q : ℚ), ∀ᵐ (ω' : Ω') ∂ν, ProbabilityTheory.mgf X (κ ω') ↑q ≤ Real.exp (↑c * ↑q ^ 2 / 2)) →
      ProbabilityTheory.Kernel.HasSubgaussianMGF X c κ ν

Defined in

Mathlib.Probability.Moments.SubGaussian

Cited by

1 results in Mathlib

Foundations

Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound