∀ {G : Type u_1} {X : Type u_2} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : AddGroup G]
  [inst_2 : AddAction G X] {ι : Type u_3} {u : Ultrafilter ι} {F : ι → Set X}
  [MeasureTheory.VAddInvariantMeasure G X μ],
  IsAddFoelner G μ (↑u) F → ∀ (g h : G) (s : Set X), IsAddFoelner.mean μ u F (g +ᵥ s) = IsAddFoelner.mean μ u F (h +ᵥ s)