∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
  m ≤ m0 →
    ∀ {f g : α → ℝ},
      MeasureTheory.StronglyMeasurable f →
        MeasureTheory.IntegrableOn f s μ →
          MeasureTheory.StronglyMeasurable g →
            MeasureTheory.IntegrableOn g s μ →
              (∀ (t : Set α), MeasurableSet t → μ t < ⊤ → ∫ (x : α) in t, g x ∂μ = ∫ (x : α) in t, f x ∂μ) →
                MeasurableSet s → μ s ≠ ⊤ → ∫ (x : α) in s, ‖g x‖ ∂μ ≤ ∫ (x : α) in s, ‖f x‖ ∂μ