Theorems · Theorem · real analysis
AbsolutelyContinuousOnInterval.intervalIntegrable_deriv
∀ {f : ℝ → ℝ} {a b : ℝ}, AbsolutelyContinuousOnInterval f a b → IntervalIntegrable (deriv f) MeasureTheory.volume a bIf f is absolutely continuous on uIcc a b, then f' is interval integrable on a..b.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- derivstatement · cited by 676
- IntervalIntegrablestatement · cited by 316
- AbsolutelyContinuousOnIntervalstatement and proof · cited by 31
- AbsolutelyContinuousOnInterval.boundedVariationOnproof · cited by 2
- BoundedVariationOn.intervalIntegrable_derivproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AbsolutelyContinuousOnInterval.integral_deriv_eq_subproof · cited by 1
- AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mulproof · cited by 1