Theorems · Theorem · real analysis
not_integrableOn_Ioi_rpow
∀ (s : ℝ), ¬MeasureTheory.IntegrableOn (fun x => x ^ s) (Set.Ioi 0) MeasureTheory.volume
The real power function with any exponent is not integrable on (0, +∞).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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_rflproof · cited by 1,558
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Set.Iooproof · cited by 1,214
- zero_lt_oneproof · cited by 598
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- zero_le_oneproof · cited by 316
- le_or_gtproof · cited by 269
- LE.le.not_gtproof · cited by 189
- LT.lt.not_gtproof · cited by 54
- Set.Ioi_subset_Ioiproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- setIntegral_Ioi_zero_rpowproof · cited by 0