In this paper, we study the Radon-Nikodým Property for the Fourier space of a commutative compact hypergroup and that of a compact (non necessarily commutative) hypergroup.  We prove the coincidence of the weak-* topology and the norm topology on the unit sphere of the subset A_K(H) of the Fourier space A(H) of a commutative hypergroup H consisting of elements that have support in a fixed compact subset K of the hypergroup H. Finally, we derive the fact that A_K(H) has the Radon-Nikodým property.




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 Lakmon, Anaté K., Etse, Kossi R., Mensah, Yaogan