Geodesic
Surface measures in infinite-dimensional spaces
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 106-114

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We construct surface measures for surfaces of codimension $n\ge1$ in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous derivative along a subspace. 
@article{MZM_1998_63_1_a10,
     author = {O. V. Pugachev},
     title = {Surface measures in infinite-dimensional spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {106--114},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a10/}
}
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O. V. Pugachev. Surface measures in infinite-dimensional spaces. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 106-114. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a10/