The main purpose of this paper is to extend the W1,p regularity results in neutron transport theory, with respect to the Lebesgue measure due to Mokhtar-Kharroubi, (1991), and to abstract measures covering, in particular, the continuous models or multigroup models. The results are obtained for vacuum boundary conditions as well as periodic boundary conditions. H2 regularity results are derived when the velocity space is endowed with an appropriate class of measures (signed in the multidimensional case).