import Mathlib


theorem intervalIntegrable_iff_intervalIntegrable_smul
    {E : Type*} [NormedAddCommGroup E]
    {a b : ℝ} {μ : MeasureTheory.Measure ℝ}
    {R : Type*} [NormedAddCommGroup R] [SMulZeroClass R E] [IsBoundedSMul R E]
    {f : ℝ → E} {r : R} (hr : r ≠ 0) :
    IntervalIntegrable f μ a b ↔ IntervalIntegrable (r • f) μ a b := by
  sorry

theorem IntervalIntegrable.abs'
    {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {f : ℝ → ℝ} (hf : Measurable f) :
    IntervalIntegrable f μ a b ↔  IntervalIntegrable (fun x => |f x|) μ a b := by
  sorry