Singular generalized functions of an infinite-dimensional argument
Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 543-551.

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It is proved that every generalized function (on a Hilbert space), concentrated on a surface of infinite codimension, is equal to zero.
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     author = {A. V. Uglanov},
     title = {Singular generalized functions of an infinite-dimensional argument},
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A. V. Uglanov. Singular generalized functions of an infinite-dimensional argument. Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 543-551. http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a9/