∀ {X : Type u_3} {Z : Type u_5} {β : Type u_6} [inst : MeasurableSpace X] [StandardBorelSpace X]
  [inst_2 : MeasurableSpace β] [inst_3 : MeasurableSpace Z] [MeasurableSpace.CountablySeparated Z] {f : X → Z},
  Measurable f → Function.Surjective f → ∀ {g : Z → β}, Measurable (g ∘ f) ↔ Measurable g