Re: simple measure theory question

ArtflDodgr (artfldodgr@xxxxxxx) wrote:


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.