Theorems · Theorem · real analysis
integrableOn_Ioi_rpow_iff
∀ {s t : ℝ}, 0 < t → (MeasureTheory.IntegrableOn (fun x => x ^ s) (Set.Ioi t) MeasureTheory.volume ↔ s < -1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Filter.univ_mem'proof · cited by 1,672
- le_rflproof · cited by 1,558
- Filter.mp_memproof · cited by 1,537
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- LE.le.trans_ltproof · cited by 795
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- zero_le_oneproof · cited by 316
- abs_of_nonnegproof · cited by 279
Cited by3
Results whose statement or proof uses this declaration.
- integrableOn_Ioi_norm_cpow_iffproof · cited by 1
- not_integrableOn_Ioi_rpowproof · cited by 1
- integrableAtFilter_rpow_atTop_iffproof · cited by 0