Theorems · Theorem · probability
ProbabilityTheory.HasSubgaussianMGF.cgf_le
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : Ω → ℝ} {c : NNReal},
ProbabilityTheory.HasSubgaussianMGF X c μ → ∀ (t : ℝ), ProbabilityTheory.cgf X μ t ≤ ↑c * t ^ 2 / 2- Defined in
- Mathlib.Probability.Moments.SubGaussian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 262 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NNRealstatement and proof · cited by 4,310
- Filter.Eventuallyproof · cited by 3,134
- NNReal.toRealstatement and proof · cited by 1,260
- ProbabilityTheory.HasSubgaussianMGFstatement and proof · cited by 36
- ProbabilityTheory.cgfstatement and proof · cited by 36
- MeasureTheory.ae_dirac_eqproof · cited by 31
- ProbabilityTheory.HasSubgaussianMGF_iff_kernelproof · cited by 9
- ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_leproof · cited by 2
- MeasureTheory.all_ae_ofproof · cited by 2
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