∀ {α : Type u_1} {β : Type u_2} (f : α → β) (x x_1 : MeasureTheory.OuterMeasure α),
  { measureOf := fun s => (x + x_1) (f ⁻¹' s), empty := ⋯, mono := ⋯, iUnion_nat := ⋯ } =
    { measureOf := fun s => x (f ⁻¹' s), empty := ⋯, mono := ⋯, iUnion_nat := ⋯ } +
      { measureOf := fun s => x_1 (f ⁻¹' s), empty := ⋯, mono := ⋯, iUnion_nat := ⋯ }