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  • 1 L.S.T.A.-Université Paris 6. Please ask the editor of the journal.
  • 2 Laboratoire de Mathématiques (UMR 6056) CNRS & Université de Reims Champagne-Ardenne & L.S.T.A.-Université Paris 6. Please ask the editor of the journal.
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We consider the minimization problem of φ-divergences between a given probability measure P and subsets Ω of the vector space M F of all signed measures which integrate a given class F of bounded or unbounded measurable functions. The vector space M F is endowed with the weak topology induced by the class F ∪ B b where B b is the class of all bounded measurable functions. We treat the problems of existence and characterization of the φ-projections of P on Ω. We also consider the dual equality and the dual attainment problems when Ω is defined by linear constraints.