Re: simple measure theory question
- From: mjhardy@xxxxxxx (Michael J Hardy)
- Date: Sat, 26 Apr 2008 02:00:03 +0000 (UTC)
ArtflDodgr (artfldodgr@xxxxxxx) wrote:
Always.
Let mu and nu denote the images of m and n under the
transformation X. For example,
mu(B) = m( X^-1}(B) )
when B is a Borel subset of the line. The absolute continuity
of m with respect to n implies the same for mu with
respect to nu, and the usual change of variables formula
for integrals then shows that the Radon-Nikodym derivative
of mu with respect to nu is the identity function.
I think you missed two points:
(1) There is a counterexample to your assertion,
which I mentioned in my initial posting;
(2) My actual question. This was found at the
bottom of my initial posting. -- Mike Hardy
PS: I think you missed what "X" is, too.
.
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