∀ {G : Type u_1} {α : Type u_3} {E : Type u_5} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α]
  [inst_3 : NormedAddCommGroup E] {s t : Set α} {μ : MeasureTheory.Measure α} [MeasurableConstVAdd G α]
  [MeasureTheory.VAddInvariantMeasure G α μ] [Countable G],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    MeasureTheory.IsAddFundamentalDomain G t μ →
      ∀ {f : α → E},
        (∀ (g : G) (x : α), f (g +ᵥ x) = f x) →
          (MeasureTheory.HasFiniteIntegral f (μ.restrict s) ↔ MeasureTheory.HasFiniteIntegral f (μ.restrict t))