  We construct surface measures in a Hilbert space endowed with a probability
measure $\nu$. The theory fits for invariant measures of some stochastic
partial differential equations such as Burgers and reaction--diffusion
equations. Other examples are weighted Gaussian measures and special product
measures $\nu$ of non Gaussian measures; in this case we exhibit a Markov
process having $\nu$ as invariant measure. In any case we prove integration by
parts formulae on sublevel sets of good functions (including spheres and
hyperplanes) that involve surface integrals.
