Lemma 1.2.3. Let $(\Omega, \bracs{\cf_t|t \ge 0}, \bp)$ be a filtered probability space, $s \ge 0$, $k \in \natp$, $L = \sum_{|\alpha| \le k}a_{\alpha} \partial^{\alpha}$ be a $\bracs{\mathcal{F}_t}$-progressively measurable random differential operator, $f \in C^{k}(\real^{d})$, and $\bracs{X_t|t \ge 0}$ be a $\real^{d}$-valued progressively measurable process, then

is a progressively measurable process.