Theorems · Theorem · measure theory
exp_neg_integrableOn_Ioi
∀ (a : ℝ) {b : ℝ}, 0 < b → MeasureTheory.IntegrableOn (fun x => Real.exp (-b * x)) (Set.Ioi a) MeasureTheory.volumeexp (-b * x) is integrable on (a, ∞).
- Defined in
- Mathlib.MeasureTheory.Integral.ExpDecay
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- nhdsproof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- Set.Ioistatement and proof · cited by 1,463
- LT.lt.ne'proof · cited by 1,417
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.Iciproof · cited by 1,070
- neg_negproof · cited by 960
- Real.expstatement and proof · cited by 871
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.exp_neg_integrableOn_Iocproof · cited by 1
- integrable_of_isBigO_exp_negproof · cited by 1