Geodesic
On the question of absolute continuity and singularity of probability measures
Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 203-221

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The basic result in this paper (Theorem 1) generalizes the well-known criterion of Kakutani to measures corresponding to arbitrary random sequences. The proof is based on Theorem 6, which gives a description of the set of convergence of a submartingale with bounded increments. The question of absolute continuity and singularity of measures corresponding to solutions of stochastic difference equations is studied. The dichotomy for Gaussian measures is obtained as a corollary. Bibliography: 13 titles. 
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Yu. M. Kabanov; R. Sh. Liptser; A. N. Shiryaev. On the question of absolute continuity and singularity of probability measures. Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 203-221. http://geodesic.mathdoc.fr/item/SM_1977_33_2_a2/