Re: simple measure theory question

Jairo Bochi (jairo.bochi@xxxxxxxxx) wrote:

You forgot to say that X is integrable.


Well, I did say parenthetically that I wanted
to consider only cases where M(x) is finite,
which amounts to the same thing.


A precise statement of your assertion is
missing. It should be something like: there
exists a real function f with domain ... such
that ... and on the points y such that ... the
derivative f'(y) exists and is ...


Here I'm not following you. I defined M and N
and said the definitions entail that M and N depend
on each other in a one-to-one way. And the derivative
I wanted to consider was dM/dN.


As for the "proof", I think you should look at
intervals of x where N(x) is strictly monotonic
**and continuous**.


I'll think about that.......


Answering your question, I believe this is not
a standard result. But once you state it precisely,
the proof will become evident.


I'm not sure there was anything wrong with the proof
I tersely sketched in my initial posting.

But it's interesting that someone who seems to
know some measure theory doesn't recognize this.

Thanks. -- Mike Hardy


.

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