Null Sets and uniform convergence

Prove that if a sequence of continous functions uniformly converges on [a,b] then the union of their graphs is a null set.

In other words:

Prove that if the sequence $\displaystyle f_n:[a,b] \to R$ converges uniformly on [a,b] then the set : $\displaystyle A=(x,f_n) | x \in [a,b],n \in N$ is a null set...

I know the function f is continous ( $\displaystyle f_n \to f $ ) and that the graph of the function f and of each $\displaystyle f_n $ if a null set....

Can't figure out how to prove what I need to prove

Thanks in advance