Let {fn} be a sequence of continuous functions on [a, b]. Suppose that for each x [a, b], {fn(x)} is a monotone decreasing sequence of real numbers. Prove that if fn rightarrow 0 pointwise on [a, b] then fn rightarrow 0 uniformly on [a, b], Dini's Theorem : Prove that if fn rightarrow f pointwise on [a, b] and f is continuous on [a, b] then fn rightarrow f uniformly on [a, b].