  For any polarized variety (X,L), we show that test configurations and, more
generally, R-test configurations (defined as finitely generated filtrations of
the section ring) can be analyzed in terms of Fubini-Study functions on the
Berkovich analytification of X with respect to the trivial absolute value on
the ground field. Building on non-Archimedean pluripotential theory, we
describe the (Hausdorff) completion of the space of test configurations, with
respect to two natural pseudo-metrics, in terms of plurisubharmonic functions
and measures of finite energy on the Berkovich space. We also describe the
Hausdorff quotient of the space of all filtrations, and establish a 1--1
correspondence between divisorial norms and divisorial measures, both being
determined in terms of finitely many divisorial valuations.
