Geodesic
The Gauss-Ostrogradskii formula in infinite-dimensional space
Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 757-770

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The aim of the present paper is to generalize the Gauss–Ostrogradskii theorem to an infinite-dimensional space $X$. On this space we consider not only Gaussian measures but a wider class of measures, differentiable along some Hilbert space continuously embedded in $X$. In the paper, a construction of a surface measure which employs ideas of the Malliavin calculus and the theory of Sobolev capacities is considered. It is a generalisation of the surface integration developed by Malliavin for the Wiener measure. 
@article{SM_1998_189_5_a5,
     author = {O. V. Pugachev},
     title = {The {Gauss-Ostrogradskii} formula in infinite-dimensional space},
     journal = {Sbornik. Mathematics},
     pages = {757--770},
     publisher = {mathdoc},
     volume = {189},
     number = {5},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/}
}
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O. V. Pugachev. The Gauss-Ostrogradskii formula in infinite-dimensional space. Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 757-770. http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/