the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...

In this talk we are first going to state the so-called ’Representation Theorem’ which provides the representation of general f -divergences in terms of the class of elementary divergences. Then we consider the risk set of a (simple versus simple) testing problem and its characterization by the above mentioned class. These ingredients enable us to prove a sharpening of the ’Range of Values Theor...