Geodesic
On absolute continuity and singularity of the distributions of random fields
Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 161-170

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A criterion is obtained for the absolute continuity or singularity of probability measures corresponding to certain classes of two-parameter discrete random fields. The proof is based on some lemmas which describe the sets of convergence of two-parameter semimartingales. Bibliography: 5 titles. 
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     author = {A. A. Gushchin},
     title = {On absolute continuity and singularity of the distributions of random fields},
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A. A. Gushchin. On absolute continuity and singularity of the distributions of random fields. Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 161-170. http://geodesic.mathdoc.fr/item/SM_1983_46_2_a1/