In this paper, we consider convex sets $K_r = \{g \ge r\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $μ$ in $H$. We first show how to define a surface measure on the level sets $\{g = r\}$ that is related to $μ$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $μ$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories