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