  In Euclidean space, the integration by parts formula for a set of finite
perimeter is expressed by the integration with respect to a type of surface
measure. According to geometric measure theory, this surface measure is
realized by the one-codimensional Hausdorff measure restricted on the reduced
boundary and/or the measure-theoretic boundary, which may be strictly smaller
than the topological boundary. In this paper, we discuss the counterpart of
this measure in the abstract Wiener space, which is a typical
infinite-dimensional space. We introduce the concept of the measure-theoretic
boundary in the Wiener space and provide the integration by parts formula for
sets of finite perimeter. The formula is presented in terms of the integration
with respect to the one-codimensional Hausdorff-Gauss measure restricted on the
measure-theoretic boundary.
