∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {f : α → α} {s : Set α}
  [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.MeasurePreserving f μ μ →
    MeasureTheory.NullMeasurableSet s μ → μ s ≠ 0 → ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ s