Geodesic
Correct discrimination of the Gaussian hypotheses
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 155-160
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Given two equivalent Gaussian weak distributions, the problem of existence of Hilbert support with continuous likelyhood ratio of these distributions is under investigation. 
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V. A. Rovsky. Correct discrimination of the Gaussian hypotheses. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 155-160. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a9/

[1] V. Sudakov, “Gaussian Measures. A Brief Survey”, Rendiconti dell'Istituto di Matematica dell'Univ. di Trieste, XXVI, suppl. (1994), 289–325 | MR | Zbl

[2] A. M. Vershik, V. N. Sudakov, “Veroyatnostnye mery v beskonechnomernykh prostranstvakh”, Zapiski nauchn. semin. LOMI, 12, 1969, 7–67 | MR | Zbl