∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} {f : α → β} {s t : Set β},
  MeasureTheory.AEDisjoint ν s t →
    MeasureTheory.Measure.QuasiMeasurePreserving f μ ν → MeasureTheory.AEDisjoint μ (f ⁻¹' s) (f ⁻¹' t)