∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] [MeasureTheory.SigmaFinite μ] {f g : α → E},
  (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → MeasureTheory.IntegrableOn f s μ) →
    (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → MeasureTheory.IntegrableOn g s μ) →
      (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, f x ∂μ = ∫ (x : α) in s, g x ∂μ) → f =ᵐ[μ] g