We consider two right-continuous indistinguishable $L^2$-martingales $U$ and $V$.
Prove that $(\int_0^uX_rdU_r)_{u \in \mathbb{R}_+}$ and $(\int_0^uX_rdV_r)_{u \in \mathbb{R}_+}$ are also indistinguishable.
I am looking for a hint to begin with to prove this fact.