Suppose $\Phi$ is a Poisson point process with intensity $\lambda(x)$. Then, for a given compact set B we have
$\Lambda({\rm B})=\int_{\rm B} \lambda(x) \rm{d} x$.
I know that $\Lambda({\rm B})$ (intensity measure) is the mean number of points falling in the region ${\rm B}$, but I don't know what $\lambda(x)$ means. how $\lambda(x)$ can be interpreted?
Moreover, consider Gaussian Poisson point process with intensity
$\lambda(x)=\frac{n}{2 \pi \sigma^2} \exp{ \frac{\|x\|^2}{2\sigma^2} }$.
In this case, what is the distribution of nodes locations, i.e., for a compact set like ${\rm B}$ how the points are distributed in each realizations of the point process and what’s the relation between $\lambda(x)$ and PDF (probability density function) of nodes locations?