Theorems · Theorem · probability

ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFun

∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ι : Type u_2} {X : ι → Ω → ℝ},
  ProbabilityTheory.iIndepFun X μ →
    ∀ {c : ι → NNReal} {s : Finset ι},
      (∀ i ∈ s, ProbabilityTheory.HasSubgaussianMGF (X i) (c i) μ) →
        ProbabilityTheory.HasSubgaussianMGF (fun ω => ∑ i ∈ s, X i ω) (∑ i ∈ s, c i) μ

Defined in: Mathlib.Probability.Moments.SubGaussian
Cited by: 2 results in Mathlib
Foundations: Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites16

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
Finsetstatement and proof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Finset.sumstatement and proof · cited by 5,195
NNRealstatement and proof · cited by 4,310
Finset.univproof · cited by 3,473
Subtype.val_injectiveproof · cited by 232
ProbabilityTheory.iIndepFunstatement and proof · cited by 138
MeasureTheory.ae_of_allproof · cited by 137
Finset.sum_attachproof · cited by 54
ProbabilityTheory.HasSubgaussianMGFstatement and proof · cited by 36

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFunproof · cited by 0
ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFunproof · cited by 0