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This problem is taken from Problem 2.4.31 (page 84) from Problems in Mathematical Analysis: Integration by W. J. Kaczor, Wiesława J. Kaczor and Maria T. Nowak.


Give an example of a bounded function $f:[0,1] \to \mathbb{R}$ which is not Riemann Integrable, but is a derivative of some function $g$ on $[0,1]$.

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Have you seen Volterra's function? –  Akhil Mathew Aug 12 '10 at 21:52
    
@Akhil Matthew: Yes i did have a look. But out of ideas. –  anonymous Aug 12 '10 at 21:54
3  
@Chandru: what's lacking? Volterra's function has exactly the properties you request. @Akhil: the link is wrong. –  Nate Eldredge Aug 12 '10 at 22:04
    
@Akhil, @Nate: I fixed the link. –  Larry Wang Aug 12 '10 at 22:26

1 Answer 1

up vote 4 down vote accepted

I gave an answer to this question on Math Overflow some months ago:

http://mathoverflow.net/questions/6711/integrability-of-derivatives/6716#6716

See, in particular, the following paper:

http://www.math.uga.edu/~pete/Goffman77.pdf

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