Let $M$ be a Brownian motion with $M_0=0$ and $V\in L(M)$. Use Lebesgue's differentiation theorem to prove that there exists a predictable process $H\in L(M)$ such that $V\cdot M$ and $H\cdot M$ are indistinguishable.
We have never worked with the Lebesgue's differentiation theorem so i don't know how i use it, especially at this Example. I would be thankful if somebody could help me.