If $\phi_c$ is a poison point process with $\lambda$ homogenous intensity, limited in a cercle C(o,R) with radius R centered in the origin. Can we write the Probability Generating Functional as bellow:
$$E\left[\prod_{x\in \phi_c} f{(x})\right]=\exp\left(-\lambda\int_{C(o,R)}\left(1-f(x)\right)dx\right)$$
Many thanks in advance.