I am having trouble finding an example of a function f:[0,1] onto Reals st f is not integrable on [0,1], but absolute value of f is integrable on [0,1]. Any suggestions?

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- April 26th 2008, 11:37 PMstudent1001[SOLVED] Ex of f not integrable
I am having trouble finding an example of a function f:[0,1] onto Reals st f is not integrable on [0,1], but absolute value of f is integrable on [0,1]. Any suggestions?

- April 26th 2008, 11:44 PMMoo
[forget it :D]

- April 27th 2008, 12:00 AMJhevon
- April 27th 2008, 12:04 AMo_O

I was thinking of that too, Jhevon although you beat me to posting it Haha.

I don't quite understand the implications of your edit though. - April 27th 2008, 12:14 AMMoo
- April 27th 2008, 12:20 AMJhevon
- April 27th 2008, 12:29 AMJhevon
- April 27th 2008, 12:30 AMMoo
- April 27th 2008, 12:31 AMJhevon
- April 27th 2008, 02:17 AMIsomorphism
- April 27th 2008, 02:44 AMCaptainBlack
You want a function from onto

Note there is no qualification on integrable. Presumably the OP is interested in something like Riemann integrability rather than Lesbegue integrability. Which is just as well as all the functions presented are Lesbegue integrable (since is countable and hence of measure zero).

RonL - April 27th 2008, 06:47 PMThePerfectHacker
This problem just does not make any sense. The way the Riemann integral is defined we use the condition that is bounded on which certainly makes it impossible for it to be onto . Unless you have a different understanding of integration, maybe you are thinking about improper integration?

- April 27th 2008, 08:03 PMCaptainBlack