Question about baire class 1 functions

[hermanni]

Hi all,
I'm a graduate student and while I was reading about measure theory I stuck at this question , can anyone help?

Let the function f: R->R be continuous except on a countable set. Show that f belongs to
Baire class 1 of functions.

For the solution I see 2 ways :
1. We need to construct a sequence f{n} from Baire -0 (set of continuous functions)
that converges to f.
2. Or we can use the fact that f belongs to Baire-n iff f^-1 (O) belongs to
Borel-n+1 the set for every O open.

Regards, h.

 

[fresh_42]

First of all, your classes are not disjoint. This is important to know, as some others exclude Baire 0 classes from Baire 1 classe, which is not the case here.

Then your first suggestion should immediately lead to the result, as you only need pointwise convergence.