Theorems · Theorem · measure theory

IntervalIntegrable.intervalIntegrable_norm_iff

∀ {E : Type u_5} [inst : NormedAddCommGroup E] {f : ℝ → E} {μ : MeasureTheory.Measure ℝ} {a b : ℝ},
  MeasureTheory.AEStronglyMeasurable f (μ.restrict (Set.uIoc a b)) →
    (IntervalIntegrable (fun t => ‖f t‖) μ a b ↔ IntervalIntegrable f μ a b)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup