 Dini's theorem

In the mathematical field of analysis, Dini's theorem says that if a monotone sequence of continuous functions converges pointwise on a compact space and if the limit function is also continuous, then the convergence is uniform.If "X" is a compact topological space, and { "f""n" } is a monotonically increasing sequence (meaning for all "n" and "x") of continuous real-valued functions on "X" which converges pointwise to a continuous function "f", then the convergence is uniform.