  The Fredholm integral equations of the first kind are a classical example of
ill-posed problem in the sense of Hadamard. If the integral operator is
self-adjoint and admits a set of eigenfunctions, then a formal solution can be
written in terms of eigenfunction expansions. One of the possible methods of
regularization consists in truncating this formal expansion after restricting
the class of admissible solutions through a-priori global bounds. In this paper
we reconsider various possible methods of truncation from the viewpoint of the
$\varepsilon$-coverings of compact sets.
