Every Hilbert subspace of a~Wiener space has measure zero
Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 369-374.

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We prove several results about measures in linear spaces. In particular we prove the assertion in the title.
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     title = {Every {Hilbert} subspace of {a~Wiener} space has measure zero},
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O. G. Smolyanov; A. V. Uglanov. Every Hilbert subspace of a~Wiener space has measure zero. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 369-374. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a6/