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 converges uniformly on [a,b] then the set : is a null set...

I know the function f is continous ( ) and that the graph of the function f and of each if a null set....

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

Thanks in advance