I want to show that if is continuous, is countable and on , then for all , .

Harking back to my days in real analysis I can show the result if we ignore the set N (ie., if the limsup is >=0 on all of [a,b]). I'm just stuck on how to 'cut out N', if you like -- I'm used to there being a measure or integral present to take care of a countable set. Any help there would be great.