∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {ι : Type u_4} {f : α → ENNReal},
  ∫⁻ (x : α), f x ∂μ ≠ ⊤ →
    ∀ {l : Filter ι} {s : ι → Set α},
      Filter.Tendsto (⇑μ ∘ s) l (nhds 0) → Filter.Tendsto (fun i => ∫⁻ (x : α) in s i, f x ∂μ) l (nhds 0)