I don't know how to solve this exercise:
Let be two measures on the borel set with (this means that is absolute continuous related to ). Prove the following statement or the contrary:
If is finite then is finite.
I'd guess that the statement is true. What's clear is that according to Radon-Nikodym there exists a measurable f such that:
and the assumption is
How can I complete this? Is there an upperbound for f I can take (a real number c)? If yes what theorem says that there is one? Then this proof was easy.
But I can't find a theorem or a corollary that says that. How can I show this?