[show abstract][hide abstract] ABSTRACT: This paper review the functional aspects of the statistical learning theory. It regards mainly the nature of the hypothesis set when no prior information is available but the data. In this framework our starting point is a discussion arguing three principles about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions and the evaluation functional on this set is a continuous mapping. Based on these principles an original theory is developed generalizing the notion of reproduction kernel Hilbert space to non hilbertian sets. Then it is shown that the hypothesis set of any learning machine has to be a generalized reproducing set. Therefore, thanks to a general "representer theorem", the solution of the learning problem is still a linear combination of some kernel. Furthermore, a way to design these kernels is given. To illustrates this framework some examples of such reproducing sets and kernels are given.