Unbounded and continuous almost everywhere

  • #1
225
0
Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?

Thanks!
 

Answers and Replies

  • #2
316
0
The function f:[0,1]->R given by
f(x) = n if x=1/n for some positive integer n
f(x) = 0 else
 
  • #4
225
0
Okay how about one which isn't Riemann (improper) integrable
 
  • #5
256
0
[tex]\displaystyle\sum_{ k = 1 }^\infty k \chi_{ [ 0, \frac{ 1 }{ k^2 } ] }[/tex]
 
  • #6
matt grime
Science Advisor
Homework Helper
9,395
3
Um, surely f(x)=1/x for x>0 and f(0)=0 is far simpler, and does everything needed.
 

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