The family Pλ of absolutely continuous probabilities w.r.t. the σ-finite measure λ is equipped with a structure of an infinite dimensional Riemannian manifold modeled on a real Hilbert. Firstly, the relation between the Hellinger distance and the Fischer metric is analysed on the positive cone Mλ+ of bounded measures absolutely continuous w.r.t. λ, appearing as a flat Riemannian manifold. Secondly, the statistical manifold Pλ is seen as a submanifold of Mλ+ and Amari-Chensov α-connections are derived. Some α-self-parallel curves are explicitely exhibited.