Re: Absolutely continuous function

In article <d650l2$c42o$1@xxxxxxxxxxxxxxxxx>, Michael
<mdergman@xxxxxxxxx> wrote:

> I'm having a lot of trouble with the following question and I'd
> appreciate any help with it :
>
> Let f be a non-increasing real-valued function on [0,1] and suppose
> that integral (from 0 to 1) of f'(x)dx = f(1) - f(0).
>
> Prove that f is absolutely continuous. I know that functions with bounded
> derivative are absolutely continuous. I also know the criterion with
> measures generated by functions being absolutely continuous wrt Lebesgue
> measure. (and of course the epsilon delta definition). Finally I know that
> the integral of the derivative of an absolutely continuous function is the
> function itself.
>
> Thank you very much for your help,
>
> Michael
>
>

The integral of the derivative of THIS function is an
absolutely continuous function. Can your prove that
that integral is this function (up to a constant)?
.

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