∀ (G : Type u_1) (α : Type u_2) [inst : SMul G α] {x : MeasurableSpace α} (μ : MeasureTheory.Measure α),
  ErgodicSMul G α μ ↔
    MeasureTheory.SMulInvariantMeasure G α μ ∧
      ∀ {s : Set α},
        MeasurableSet s → (∀ (g : G), (fun x => g • x) ⁻¹' s =ᵐ[μ] s) → Filter.EventuallyConst s (MeasureTheory.ae μ)