Theorems · Theorem · probability
ProbabilityTheory.integrable_exp_mul_of_le
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ] {X : Ω → ℝ}
(t b : ℝ),
0 ≤ t → AEMeasurable X μ → (∀ᵐ (ω : Ω) ∂μ, X ω ≤ b) → MeasureTheory.Integrable (fun ω => Real.exp (t * X ω)) μ- Defined in
- Mathlib.Probability.Moments.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites19
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
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.Integrablestatement · cited by 1,367
- le_of_ltproof · cited by 1,175
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Real.expstatement and proof · cited by 871
- AEMeasurablestatement and proof · cited by 840
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