∀ {X : Type u_3} {Y : Type u_4} {α : Type u_5} [inst : Zero α] [inst_1 : TopologicalSpace X]
  [inst_2 : TopologicalSpace Y] [inst_3 : MeasurableSpace X] [inst_4 : MeasurableSpace Y] [OpensMeasurableSpace X]
  [OpensMeasurableSpace Y] [inst_7 : PseudoMetricSpace α] {f : X × Y → α},
  Continuous f → HasCompactSupport f → ∀ {ε : ℝ}, 0 < ε → ∃ g, ∀ (x : X × Y), dist (f x) (g x) < ε