Theorems · Theorem · probability
ProbabilityTheory.HasSubgaussianMGF.add
∀ {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.HasSubgaussianMGF (fun ω => X ω + Y ω) ((NNReal.sqrt cX + NNReal.sqrt cY) ^ 2) μ- Defined in
- Mathlib.Probability.Moments.SubGaussian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NNRealstatement and proof · cited by 4,310
- OrderIsostatement · cited by 874
- MeasureTheory.Measure.diracproof · cited by 210
- ProbabilityTheory.Kernel.constproof · cited by 93
- NNReal.sqrtstatement and proof · cited by 91
- ProbabilityTheory.Kernel.HasSubgaussianMGFproof · cited by 36
- ProbabilityTheory.HasSubgaussianMGFstatement and proof · cited by 36
- ProbabilityTheory.HasSubgaussianMGF_iff_kernelproof · cited by 9
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