∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
  [BorelSpace α] [inst_3 : MeasurableSpace β] [inst_4 : TopologicalSpace β] [BorelSpace β] (f : α ≃ₜ β),
  (MeasureTheory.Measure.map (⇑f) μ).InnerRegular ↔ μ.InnerRegular