Let $M$ be a Poisson Random Measure (PRM) having an intensity $\rho$. Let $g$ be a measurable function and non-negative. And then let's denote $M(g)$ as the integral with respect to $M$.
How can we show $$E(M(g)M(f)) = \rho(gf) + \rho(g)\rho(f)$$
My intuition is that we can use the laplace functional of $M$ to show this but I'm having trouble in how to use it?