∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Mul G] [MeasurableMul G] (μ : MeasureTheory.Measure G)
  [μ.IsMulLeftInvariant] (g : G) {X : Type u_3} [inst_4 : MeasurableSpace X] {μ' : MeasureTheory.Measure X} {f : X → G},
  MeasureTheory.MeasurePreserving f μ' μ → MeasureTheory.MeasurePreserving (fun x => g * f x) μ' μ