∀ {α : Type u_2} {β : Type u_3} {δ : Type u_5} {m0 : MeasurableSpace α} [inst : MeasurableSpace β]
  [inst_1 : MeasurableSpace δ] {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure δ} {f : α → δ} {g : δ → β},
  AEMeasurable g ν → MeasureTheory.Measure.QuasiMeasurePreserving f μ ν → AEMeasurable (g ∘ f) μ