∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} {f : α → γ} {g : β → γ}
  [inst_3 : TopologicalSpace γ] [TopologicalSpace.PseudoMetrizableSpace γ] [BorelSpace γ],
  ProbabilityTheory.IdentDistrib f g μ ν →
    MeasureTheory.AEStronglyMeasurable f μ → MeasureTheory.AEStronglyMeasurable g ν