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Theorems · Theorem · real analysis

AbsolutelyContinuousOnInterval.intervalIntegrable_deriv

∀ {f : ℝ → ℝ} {a b : ℝ}, AbsolutelyContinuousOnInterval f a b → IntervalIntegrable (deriv f) MeasureTheory.volume a b

If f is absolutely continuous on uIcc a b, then f' is interval integrable on a..b.

Defined in
Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable
Cited by
2 results in Mathlib
Foundations
Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

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