  We study properties of a generalization of the Mahler measure to elements in
group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus
is the variation of the Mahler measure when the base group is changed. In
particular, we study how to obtain the Mahler measure over an infinite group as
limit of Mahler measures over finite groups, for example, in the classical case
of the free abelian group or the infinite dihedral group, and others.
