Let $(X_t)_{t \ge 0}$ be a Lévy process on $\mathbb R$ with Lévy measure $\nu$.

Define the jump counting measure $N(t, A) = \lvert\{s \in [0, t] \mathrel: \Delta X_s \in A\}\rvert$ where $\Delta X_s$ denotes the jump height at time $s$.

For a fixed Borel set $A$ such that $0 \notin A$, let $N_t = N(t,A)$.

How can I prove that $E[N_t] = t\nu(A)$?