Theorems · Theorem · probability
ProbabilityTheory.HasSubgaussianMGF_iff_kernel
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : Ω → ℝ} {c : NNReal},
ProbabilityTheory.HasSubgaussianMGF X c μ ↔
ProbabilityTheory.Kernel.HasSubgaussianMGF X c (ProbabilityTheory.Kernel.const Unit μ)
(MeasureTheory.Measure.dirac ())- Defined in
- Mathlib.Probability.Moments.SubGaussian
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- ENNRealproof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- Filter.Eventuallyproof · cited by 3,134
- MeasureTheory.aeproof · cited by 2,352
- one_smulproof · cited by 1,374
- MeasureTheory.Integrableproof · cited by 1,367
- NNReal.toRealproof · cited by 1,260
- Real.expproof · cited by 871
Cited by9
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasSubgaussianMGF.measure_ge_leproof · cited by 4
- ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGFproof · cited by 2
- ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mulproof · cited by 1
- ProbabilityTheory.HasSubgaussianMGF.negproof · cited by 1
- ProbabilityTheory.HasSubgaussianMGF.congrproof · cited by 1
- ProbabilityTheory.HasSubgaussianMGF.addproof · cited by 0
- ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zeroproof · cited by 0
- ProbabilityTheory.HasSubgaussianMGF.cgf_leproof · cited by 0
- ProbabilityTheory.HasSubgaussianMGF.const_mulproof · cited by 0