The current-current correlation function plays a crucial role in the
Mott theory of conductivity for disordered systems. We prove a Pastur-Shubin-type formula for the current-current correlation function 02expressing it as a thermodynamic limit. We prove that the limit is
independent of the self-adjoint boundary conditions and independent of a
large family of expanding regions. We relate this ^nite-volume de^nition
to the de^nition obtained by using the in^nite-volume operators and the
trace-per-unit volume.