# Uniform convergence

1. Dec 3, 2007

### lola21

1. The problem statement, all variables and given/known data
Suppose:
fn goes to f pointwise on [a,b]
For each c in (a,b) fn goes to f uniformly on (c,b), and for some M, fn(x) is less than M for all n, all x in [a,b]
Prove fn goes to f uniformly on [a,b]

2. Relevant equations

3. The attempt at a solution
I think I proved that we can choose c sufficiently close to a such that fn converges to f uniformly on (a,b). I can't see how to show that fn converges uniformly when we include the endpoints. Is more information necessary? If so, what do we need to know?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution