Theorems · Theorem · probability

ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_le

∀ {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 →
    ∀ᵐ (ω' : Ω') ∂ν, ∀ (t : ℝ), ProbabilityTheory.cgf X (κ ω') t ≤ ↑c * t ^ 2 / 2

Defined in

Mathlib.Probability.Moments.SubGaussian

Cited by

2 results in Mathlib

Foundations

Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound