∀ {α : Type u_1} {ι : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {l : Filter ι}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] [l.IsCountablyGenerated] {φ : ι → Set α},
  MeasureTheory.AECover μ l φ →
    ∀ {f : α → E},
      MeasureTheory.Integrable f μ → Filter.Tendsto (fun i => ∫ (x : α) in φ i, f x ∂μ) l (nhds (∫ (x : α), f x ∂μ))