  The volume of a line bundle is defined in terms of a limsup. It is a
fundamental question whether this limsup is a limit. It has been shown that
this is always the case on generically reduced schemes. We show that volumes
are limits in two classes of schemes that are not necessarily generically
reduced: codimension one subschemes of projective varieties such that their
components of maximal dimension contain normal points and projective schemes
whose nilradical squared equals zero.
