Non-homogeneous Poisson point process

Let $\lambda$ be a nonnegative measurable intensity function on a space with reference measure $dx$. A Non-homogeneous Poisson point process has independent counts on disjoint measurable sets andwhenever the integral is finite.

The intensity function $\lambda$ is the density of the expected counting measure: $\mathbb{E}[N(A)]={\int }_A\lambda (x)dx$.