∀ {α : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {G : Type u_4} [inst : InvolutiveInv G]
  [inst_1 : MeasurableSpace G] [MeasurableInv G] {f : α → G}, AEMeasurable (fun x => (f x)⁻¹) μ = AEMeasurable f μ