In this paper we study dually flat spaces arising from Delzant polytopes equipped with symplectic potential together with the corresponding toric Kahler manifold as its torification. We introduce a dually flat structure and the associated Bregman divergence on the boundary from the view point of toric Kahler geometry. We show a continuity and an extended Pythagorean theorem for the divergence on the boundary. We also provide a characterization for toric Kahler manifold to become a torification of a mixture family on a finite set.

翻译：暂无翻译