  In this paper we study dually flat spaces arising from Delzant polytopes
equipped with a symplectic potential together with their corresponding toric
K\"ahler manifolds as their torifications.We introduce a dually flat structure
and the associated Bregman divergence on the boundary from the viewpoint of
toric K\"ahler geometry. We show a continuity and a generalized Pythagorean
theorem for the divergence on the boundary. We also provide a characterization
for a toric K\"ahler manifold to become a torification of a mixture family on a
finite set.
