Theorems · Theorem · real analysis
integrableOn_Ioi_cpow_iff
∀ {s : ℂ} {t : ℝ}, 0 < t → (MeasureTheory.IntegrableOn (fun x => ↑x ^ s) (Set.Ioi t) MeasureTheory.volume ↔ s.re < -1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Complex.restatement and proof · cited by 882
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- MeasureTheory.Integrable.normproof · cited by 63
- integrableOn_Ioi_cpow_of_ltproof · cited by 3
- integrableOn_Ioi_norm_cpow_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- not_integrableOn_Ioi_cpowproof · cited by 1