Let $\xi$ be a point process and $\mu$ its intensity measure, i.e. $\mu(\cdot)=\mathbb{E}[\xi(\cdot)]$. The Laplace transform of $\mu$:
$\mathcal{L}\mu(z)=\int_{0}^{\infty}e^{-zx}\mu(dx)$
converges for all $z\in\mathbb{C}$ absolutely.
Does anyone know which (absolut) convergence criterion to use here?
And what does the Laplace transformation do with the intensity measure here? Is there any way to visualize this?