 The test is as follows.Let {"g""n"} be a uniformly bounded sequence of real-valued continuous functions on a set "E" such that "g""n"+1("x") ≤ "g""n"("x") for all "x" ∈ "E" and positive integers "n", and let {"f""n"} be a sequence of real-valued functions such that the series Σ"f""n"("x") converges uniformly on "E".Then Σ"f""n"("x")"g""n"("x") converges uniformly on "E".