Sunday, 19 October 2014

real analysis - If f is absolutely continuous sqrt(f) may not be

The problem reads:



Prove that if f:[0,1](0,) is absolutely continuous f may not be.




I am having trouble figuring out how to show this. I found that x2sin(1x2) is not absolutely continuous, but then I need to show that [x2sin(1x2)]2 is absolutely continuous and I don't think that it is. Is there a more general way to show this or is there a counterexample that works?

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