Theorems · Definition · probability
ProbabilityTheory.mgf
{Ω : Type u_1} → {m : MeasurableSpace Ω} → (Ω → ℝ) → MeasureTheory.Measure Ω → ℝ → ℝMoment-generating function of a real random variable X: fun t => μ[exp(t*X)].
- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 250 from the axioms, rests on 6,485 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- MeasureTheory.integralproof · cited by 1,779
- Real.expproof · cited by 871
Cited by118
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cgfproof · cited by 36
- ProbabilityTheory.Kernel.HasSubgaussianMGF.mgf_lestatement · cited by 13
- ProbabilityTheory.HasSubgaussianMGF_iff_kernelproof · cited by 9
- ProbabilityTheory.mgf_pos'statement · cited by 9
- ProbabilityTheory.exp_cgfstatement and proof · cited by 8
- ProbabilityTheory.mgf_zero'statement · cited by 7
- ProbabilityTheory.mgf_zero_measurestatement · cited by 6
- ProbabilityTheory.mgf_id_mapstatement and proof · cited by 5
- ProbabilityTheory.mgf_nonnegstatement · cited by 5
- ProbabilityTheory.Kernel.HasSubgaussianMGF.congrproof · cited by 4
- ProbabilityTheory.HasSubgaussianMGF.mgf_lestatement · cited by 4
- ProbabilityTheory.deriv_cgfstatement and proof · cited by 4