Prove for the following set of conditions that there is a subsequence f_k(x) that converges to a continuous function f(x):
1. f_k(x) is an infinite sequence of functions from the interval [0,1] to the set of real numbers.
2. The sequence is uniformly bounded, i.e. there exists some R<infty s.t. |f_k(x)|<R for all x,k.
3. The sequence is equicontinuous at every x.
