Theorems · Theorem · probability
ProbabilityTheory.iIndepFun.integrable_exp_mul_sum
∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {t : ℝ}
[MeasureTheory.IsFiniteMeasure μ] {X : ι → Ω → ℝ},
ProbabilityTheory.iIndepFun X μ →
(∀ (i : ι), Measurable (X i)) →
∀ {s : Finset ι},
(∀ i ∈ s, MeasureTheory.Integrable (fun ω => Real.exp (t * X i ω)) μ) →
MeasureTheory.Integrable (fun ω => Real.exp (t * (∑ i ∈ s, X i) ω)) μ- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Finset.sumstatement and proof · cited by 5,195
- MulZeroClass.mul_zeroproof · cited by 2,091
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Real.expstatement and proof · cited by 871
- Finset.sum_applyproof · cited by 234
- Finset.sum_insertproof · cited by 196
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