Theorems · Definition · probability
ProbabilityTheory.cgf
{Ω : Type u_1} → {m : MeasurableSpace Ω} → (Ω → ℝ) → MeasureTheory.Measure Ω → ℝ → ℝCumulant-generating function of a real random variable X: fun t => log μ[exp(t*X)].
- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 251 from the axioms · 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
- Real.logproof · cited by 939
- ProbabilityTheory.mgfproof · cited by 113
Cited by36
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cgf_zero_measurestatement · cited by 12
- ProbabilityTheory.exp_cgfstatement · cited by 8
- ProbabilityTheory.deriv_cgfstatement and proof · cited by 4
- ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_lestatement · cited by 2
- ProbabilityTheory.analyticAt_cgfstatement and proof · cited by 2
- ProbabilityTheory.analyticOn_cgfstatement · cited by 1
- ProbabilityTheory.cgf_zerostatement · cited by 1
- ProbabilityTheory.cgf_zero'statement · cited by 1
- ProbabilityTheory.deriv_cgf_zerostatement · cited by 1
- ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zeroproof · cited by 1
- ProbabilityTheory.iteratedDeriv_two_cgfstatement and proof · cited by 1
- ProbabilityTheory.iteratedDeriv_two_cgf_eq_integralstatement and proof · cited by 1