Theorems · Theorem · probability

ProbabilityTheory.HasSubgaussianMGF.add_of_indepFun

∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X Y : Ω → ℝ} {cX cY : NNReal},
  ProbabilityTheory.HasSubgaussianMGF X cX μ →
    ProbabilityTheory.HasSubgaussianMGF Y cY μ →
      ProbabilityTheory.IndepFun X Y μ → ProbabilityTheory.HasSubgaussianMGF (fun ω => X ω + Y ω) (cX + cY) μ

Defined in: Mathlib.Probability.Moments.SubGaussian
Cited by: 1 results in Mathlib
Foundations: Depth 272 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
TopologicalSpaceproof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
NNRealstatement and proof · cited by 4,310
MeasureTheory.Integrableproof · cited by 1,367
NNReal.toRealproof · cited by 1,260
le_of_ltproof · cited by 1,175
Real.expproof · cited by 871
mul_addproof · cited by 413
ContinuousENormproof · cited by 290
ProbabilityTheory.IndepFunstatement and proof · cited by 192

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.HasSubgaussianMGF.sub_of_indepFunproof · cited by 1