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About the absolute continuity and orthogonality for two probability measures



We give necessary and sufficient conditions for two probability measures to be absolute continuous or orthogonal. In many cases, these conditions can be easily checked and, in certain circumstances, it may be presented in terms of [chi]2-distances. This work extends results obtained in Dion and Ferland (J. Statist. Planning Inference 43 (1995) 235), Kabanov et al. (Math. USSR-Sb 33 (2) (1977) 203), and Skouras (J. Statist. Planning Inference 75 (1998) 1)

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