∀ {α : Type u_1} {β : Type u_2} [inst : Lattice α] [inst_1 : Group α] [inst_2 : MeasurableSpace α]
  [inst_3 : MeasurableSpace β] {f : β → α} [MeasurableInv α] [MeasurableSup₂ α] {μ : MeasureTheory.Measure β},
  AEMeasurable f μ → AEMeasurable (fun x => |f x|ₘ) μ