  We show that the results proved by Simon on the canonical retraction $F_M$
from the space of $M$-invariant types onto the space of types finitely
satisfiable in $M$ remain true over measures. We also make another construction
of the canonical retraction for measures, mimicking what Simon did for types,
and show that it coincides with Simon's canonical retraction for measures. To
do so, we make extensive use of smooth measures.
