Unbounded and continuous almost everywhere

1. Feb 27, 2009

Ja4Coltrane

Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?

Thanks!

2. Feb 27, 2009

yyat

The function f:[0,1]->R given by
f(x) = n if x=1/n for some positive integer n
f(x) = 0 else

3. Feb 27, 2009

Ja4Coltrane

muchas gracias

4. Feb 27, 2009

Ja4Coltrane

Okay how about one which isn't Riemann (improper) integrable

5. Mar 15, 2009

rochfor1

$$\displaystyle\sum_{ k = 1 }^\infty k \chi_{ [ 0, \frac{ 1 }{ k^2 } ] }$$

6. Mar 15, 2009

matt grime

Um, surely f(x)=1/x for x>0 and f(0)=0 is far simpler, and does everything needed.