∀ {Ω : Type u_1} {ι : Type u_2} [inst : MeasurableSpace Ω] {S : Set (Set Ω)},
  IsPiSystem S →
    ∀ {μ : ι → MeasureTheory.ProbabilityMeasure Ω} {ν : MeasureTheory.ProbabilityMeasure Ω} {l : Filter ι}
      {t : Finset (Set Ω)},
      (∀ s ∈ t, s ∈ S) →
        (∀ s ∈ S, MeasurableSet s) →
          (∀ s ∈ S, Filter.Tendsto (fun i => (μ i) s) l (nhds (ν s))) →
            Filter.Tendsto (fun i => (μ i) (⋃ s ∈ t, s)) l (nhds (ν (⋃ s ∈ t, s)))