On integration by parts formula on open convex sets in Wiener spaces

In Euclidean space, it is well known that any integration by parts formula for a set of finite perimeter \(\Omega \) expressed the with respect to measure \(P(\Omega ,\cdot )\) which equivalent one-codimensional Hausdorff restricted reduced boundary \). The same result has been proved in an abstract Wiener typically infinite-dimensional where surface considered spherical Hausdorff–Gauss \(\mathscr {S}^{\infty -1}\) measure-theoretic this paper, we consider open convex and provide explicit density -1}\). particular, can be written terms Minkowski functional \(\mathfrak {p}\) inner point As consequence, obtain sets spaces.