Uniform convergence

[Tolaso J Kos]

Let \( f_n \) be a sequence of continuous functions on an interval \( [a, b] \). Suppose that for any \( x \in [a, b] \) \( f_n (x) \) is non increasing . Show that if \( f_n \) converges point to point to the zero function then \( f_n \) converges uniformly to the zero function on \( [a, b] \).