∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β],
  (∀ x ∈ s, ∃ t ∈ nhdsWithin x s, HasSumUniformlyOn f g t) → HasSumLocallyUniformlyOn f g s