  The Mahler measure of a function on the real d-torus is its geometric mean
over the torus. It appears in number theory, ergodic theory and other fields.
The Fuglede-Kadison determinant is defined in the context of von Neumann
algebra theory and can be seen as a noncommutative generalization of the Mahler
measure. In the paper we discuss and compare theorems in both fields,
especially approximation theorems by finite dimensional determinants. We also
explain how to view Fuglede-Kadison determinants as continuous functions on the
space of marked groups.
