Theorems · Theorem · measure theory

intervalIntegral.continuousOn_primitive_interval

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {μ : MeasureTheory.Measure ℝ}
  {f : ℝ → E} [MeasureTheory.NullSingletonClass μ],
  MeasureTheory.IntegrableOn f (Set.uIcc a b) μ → ContinuousOn (fun x => ∫ (t : ℝ) in a..x, f t ∂μ) (Set.uIcc a b)

Defined in

Mathlib.MeasureTheory.Integral.DominatedConvergence

Cited by

2 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.NullSingletonClass