Let $E$ be a normed $\mathbb R$-vector space and $$\Omega:=\{\omega:[0,\infty)\to E\mid\omega\text{ is càdlàg}\}.$$ Moreover, let $$\pi_t:\Omega\to E\;,\;\;\;\omega\mapsto\omega(t)$$ and $$\mathcal F_t:=\sigma(\pi_s,s\le t)$$ for $t\ge0$.
Let $B\in\mathcal B(E)$ with $0\not\in\overline B$. Are able to show that $$\tau(\omega):=\inf\{t>0:\Delta\omega(t)\in B\}\;\;\;\text{for }\omega\in\Omega$$ is a stopping time with respect to the filtration $(\mathcal F_t)_{t\ge0}$?
As usual, $\omega(0-):=0$, $$\omega(t-):=\lim_{s\to t-}\omega(s)$$ and $$\Delta\omega(t):=\omega(t)-\omega(t-)$$ for $\omega\in\Omega$.