∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
  MeasureTheory.AEStronglyMeasurable f μ →
    0 ≤ᵐ[μ] f → (∫⁻ (a : α), ENNReal.ofReal (f a) ∂μ ≠ ⊤ ↔ MeasureTheory.Integrable f μ)