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

Construction of a surface integral under local Malliavin assumption and integration by parts formulae