∀ {α : Type u_1} {M : Type u_2} [inst : MeasurableSpace α] [inst_1 : AddCommMonoid M] {f : α → α}
  {μ : MeasureTheory.Measure α} {φ ψ : α → M},
  MeasureTheory.Measure.QuasiMeasurePreserving f μ μ → φ =ᵐ[μ] ψ → ∀ (n : ℕ), birkhoffSum f φ n =ᵐ[μ] birkhoffSum f ψ n