hermanni
Oct17-10, 01:36 PM
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.
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.