Metric and probabilistic information associated with Fredholm integral equations of the first kind

The problem of evaluating the information associated with Fredholm integral equations of the first kind, when the integral operator is self-- adjoint and compact, is considered here. The data function is assumed to be perturbed {\it gently} by an additive noise so that it still belongs to the range of the operator. First we estimate upper and lower bounds for the $\epsilon$--capacity (and then for the {\it metric information}), and explicit computations in some specific cases are given; then the problem is reformulated from a probabilistic viewpoint and use is made of the probabilistic information theory. The results obtained by these two approaches are then compared.