∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {f : α → γ} {g : β → γ}
  {μ : autoParam (MeasureTheory.Measure α) ProbabilityTheory.IdentDistrib._auto_1}
  {ν : autoParam (MeasureTheory.Measure β) ProbabilityTheory.IdentDistrib._auto_3},
  ProbabilityTheory.IdentDistrib f g μ ν → MeasureTheory.Measure.map f μ = MeasureTheory.Measure.map g ν