∀ {α : Type u_2} {β : Type u_1} {mα : MeasurableSpace α} [inst : MeasurableSpace β]
  (f : MeasureTheory.OuterMeasure α →ₗ[ENNReal] MeasureTheory.OuterMeasure β),
  (∀ (μ : MeasureTheory.Measure α), inst ≤ (f μ.toOuterMeasure).caratheodory) →
    ∀ (c : ENNReal) (μ : MeasureTheory.Measure α), inst ≤ (f (c • μ).toOuterMeasure).caratheodory