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From: Maury Barbato on 2 Dec 2009 03:08
Hello,
let f:R->R be a Lipschitz function. It's a well-known
fact that f is almost everywhere differentiable.
Anyhow, I think f' doesn't need to be almost everywhere
continuous.
What do you think about?

Thank you very much for your attention.
My Best Regards,
Maury Barbato
From: Gc on 2 Dec 2009 15:08
On 2 joulu, 20:08, Maury Barbato <mauriziobarb...(a)aruba.it> wrote:
> Hello,
> let f:R->R be a Lipschitz function. It's  a well-known
> fact that f is almost everywhere differentiable.
> Anyhow, I think  f' doesn't need to be almost everywhere
> continuous.
> What do you think about?

I think you are right. Check Volterra`s function. The
http://en.wikipedia.org/wiki/Volterra%27s_function


> Thank you very much for your attention.
> My Best Regards,
> Maury Barbato

From: Maury Barbato on 3 Dec 2009 00:10
Gc wrote:

> On 2 joulu, 20:08, Maury Barbato
> <mauriziobarb...(a)aruba.it> wrote:
> > Hello,
> > let f:R->R be a Lipschitz function. It's  a
> well-known
> > fact that f is almost everywhere differentiable.
> > Anyhow, I think  f' doesn't need to be almost
> everywhere
> > continuous.
> > What do you think about?
>
> I think you are right. Check Volterra`s function. The
> http://en.wikipedia.org/wiki/Volterra%27s_function
>
>
> > Thank you very much for your attention.
> > My Best Regards,
> > Maury Barbato
>

Very good example, it works perfectly!
Thank you very very much Gc for your great help!

My Best Regards,
Maury Barbato
From: David C. Ullrich on 3 Dec 2009 10:42
On Wed, 02 Dec 2009 13:08:04 EST, Maury Barbato
<mauriziobarbato(a)aruba.it> wrote:

>Hello,
>let f:R->R be a Lipschitz function. It's a well-known
>fact that f is almost everywhere differentiable.
>Anyhow, I think f' doesn't need to be almost everywhere
>continuous.

That's correct. If g is any bounded measurable function
and you define f(x) = int_0^x g(t) dt then f is Lipschitz
and f' = g almost everywhere.

>What do you think about?
>
>Thank you very much for your attention.
>My Best Regards,
>Maury Barbato

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
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