∀ {ι : Type u_1} {M : Type u_3} {X : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace M]
  [inst_2 : AddCommMonoid M] [ContinuousAdd M] {f : ι → X → M},
  (∀ (i : ι), Continuous (f i)) →
    (LocallyFinite fun i => Function.support (f i)) → Continuous fun x => ∑ᶠ (i : ι), f i x