For a Poisson point process $e=(e(t),t\geq 0)$ taking values in $E\cup \{\gamma\}$, there is an integral in the compensation formula, which I do not quite understand, namely $$ \int_0^\infty dt \int_E dv(\eta)H_t(\eta), $$ where $H=(G_t,t\geq 0)$ is a predictable process taking values in the space of non negative measurable functions on $E\cup\{\gamma\}$ such that $H_t(\gamma)=0$ for all $t\geq0$, $E$ is a Polish space and $v$ is a sigma-finite measure on $E$.
Is it the same as $$ \int_0^\infty \Big( \int_E H_t(\eta)dv(\eta)\Big) dt? $$
If not, what is the difference?
Thank you very much.