Semimartingales are closed under absolutely continuous measure change.

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I am seeking a validation, correction and hopefully a reference for the following (repaired?) claim. It comes from guessing from the properties section of semimartingales at wikipedia.

Let $S$ be a $P$-semimartingale and let $M$ be a (strictly) positive, unit-initialized $P$-martingale. Let $T<\infty$.

Then if $A$ is t-measurable through $Q(A)=E[1_A M_t ]$ $M$ defines a measure change to an equivalent measure $Q$ and $S$ is also a $Q$-semimartingale. Since $1/M_T$ is trivially a $Q$-martingale going in the other directions, any $Q$-semimartingale is a $P$-semimartingale. (<- Edit: Last appearance there i accidently wrote $P$-martingale, thanks!)

I.e. the class of semimartingales is closed with respect to equivalent measure changes.

Edit: Limit Theorems of Stochastic Processes Theorem 3.13 appears to work.