∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {φ : ℕ → Set α},
  MeasureTheory.AECover μ Filter.atTop φ →
    Monotone φ →
      ∀ {f : α → ENNReal},
        AEMeasurable f μ → Filter.Tendsto (fun i => ∫⁻ (x : α) in φ i, f x ∂μ) Filter.atTop (nhds (∫⁻ (x : α), f x ∂μ))