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This paper is devoted to show some results of harmonic analysis on perfect hypergroups. We give some ways to preserve the perfectness of hypergroups, under different kinds of transformations. We state and prove some properties of the set of Radon measures on the dual hypergroups. Also we explain some exact conditions on translation operators to translate perfect hypergroups, to another perfect hypergroups. Details computations with implemented formal examples are explicitly introduced. 

hypergroups, Radon measure, positive definite.