  We construct an infinite-dimensional information manifold based on
exponential Orlicz spaces without using the notion of exponential convergence.
We then show that convex mixtures of probability densities lie on the same
connected component of this manifold, and characterize the class of densities
for which this mixture can be extended to an open segment containing the
extreme points. For this class, we define an infinite-dimensional analogue of
the mixture parallel transport and prove that it is dual to the exponential
parallel transport with respect to the Fisher information. We also define
{\alpha}-derivatives and prove that they are convex mixtures of the extremal
(\pm 1)-derivatives.
