On conditions for absolute continuity of probability measures
Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 697-707

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A number of sufficient conditions are obtained for the absolute continuity of probability measures under the assumption that their restrictions to some increasing system of $\sigma$-algebras are absolutely continuous. An example is given which shows that these conditions are close to being best possible. Bibliography: 7 titles.
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A. A. Novikov. On conditions for absolute continuity of probability measures. Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 697-707. http://geodesic.mathdoc.fr/item/SM_1979_35_5_a4/