Theorems · Theorem · probability
ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul
∀ {Ω : Type u_1} {m mΩ : MeasurableSpace Ω} {hm : m ≤ mΩ} [inst : StandardBorelSpace Ω] {μ : MeasureTheory.Measure Ω}
[inst_1 : MeasureTheory.IsFiniteMeasure μ] {X : Ω → ℝ} {c : NNReal},
ProbabilityTheory.HasCondSubgaussianMGF m hm X c μ →
∀ (t : ℝ) (p : NNReal), MeasureTheory.MemLp (fun ω => Real.exp (t * X ω)) (↑p) μ- Defined in
- Mathlib.Probability.Moments.SubGaussian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- ENNReal.ofNNRealstatement · cited by 1,279
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Real.expstatement · cited by 871
- MeasureTheory.MemLpstatement · cited by 457
- StandardBorelSpacestatement and proof · cited by 304
- ProbabilityTheory.HasCondSubgaussianMGFstatement and proof · cited by 15
- ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mulproof · cited by 4
- ProbabilityTheory.condExpKernel_comp_trimproof · cited by 4
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