Deformed Exponential And The Behavior Of The Normalizing Function

In this paper we consider the statistical manifold defined in terms of a deformed exponential phi. For the non-atomic case we establish a relation between the behavior of the deformed exponential function and the Delta(2)-condition and analyze the comportment of the normalizing function near to the boundary of its domain. In the purely atomic case we find an equivalent condition to the behavior that characterizes the deformed exponential discussed in this work. Moreover, we prove a consequence from the fact the Musielak-Orlicz function does not satisfy the delta(2)-condition.