Theorems · Theorem · special functions
integrableOn_rpow_mul_exp_neg_mul_rpow
∀ {p s b : ℝ},
-1 < s →
0 < p → 0 < b → MeasureTheory.IntegrableOn (fun x => x ^ s * Real.exp (-b * x ^ p)) (Set.Ioi 0) MeasureTheory.volume- Cited by
- 1 results in Mathlib
- Foundations
- Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.expstatement and proof · cited by 871
- neg_mulproof · cited by 654
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- le_of_not_gtproof · cited by 430
- inv_mul_cancel₀proof · cited by 267
Cited by1
Results whose statement or proof uses this declaration.
- integrableOn_rpow_mul_exp_neg_mul_sqproof · cited by 1