Let $W$ be a standard Brownian motion on $(\Omega, \mathcal{F}, (\mathcal{F}_t)_{t \geq 0}, \mathbb{P})$, where $(\mathcal{F}_t)$ is the natural filtration of $W$. Then every $(\mathcal{F}_t)$-local martingale $M$ can be written as \begin{align*} M_t = M_0 + \int_0^t H_s \, dW_s \end{align*} for some $(\mathcal{F}_t)$-previsible process $H$ with $\int_0^t H_s^2 \, ds < \infty$ a.s. for all $t$.