Below is Theorem 4 and its proof from the following post : https://almostsuremath.com/2010/05/03/girsanov-transformations/
Here, we have measures $Q$ and $P$ equivalent, and $U$ is the Radon-Nikodym derivative of $Q$ with respect to $P$, i.e. $U=dQ/dP$. Then we have $U^{-1}=dP/dQ$ and we know that $U^{-1}$ is a uniformly integrable martingale with respect to $Q$.
Now, given a local martingale $X$ with respect to $P$, we define a process $V$ by $$V=\int U^{-1} d[U,X].$$
The author merely states that $V$ is a FV process, but I can't figure out why. What properties allow us to conclude immediately that $V$ has finite variation?
