Theorems · Theorem · real analysis

intervalIntegral.differentiable_integral_of_continuous

∀ {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {f : ℝ → E} {a : ℝ},
  Continuous f → Differentiable ℝ fun u => ∫ (x : ℝ) in a..u, f x

The integral of a continuous function is differentiable on a real set s.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus

Cited by

1 results in Mathlib

Foundations

Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace