∀ {ι : Type u_1} {α : ι → Type u_2} {mα : (i : ι) → MeasurableSpace (α i)}
  {P : (J : Finset ι) → MeasureTheory.Measure ((j : ↥J) → α ↑j)} {s t : Set ((i : ι) → α i)},
  MeasureTheory.IsProjectiveMeasureFamily P →
    s ∈ MeasureTheory.measurableCylinders α →
      t ∈ MeasureTheory.measurableCylinders α →
        Disjoint s t →
          MeasureTheory.projectiveFamilyFun P (s ∪ t) =
            MeasureTheory.projectiveFamilyFun P s + MeasureTheory.projectiveFamilyFun P t