  The fundamental Filippov-Wazwski Relaxation Theorem states that the solution
set of an initial value problem for a locally Lipschitz inclusion is dense in
the solution set of the same initial value problem for the corresponding
relaxation inclusion on compact intervals. In our recent work, a complementary
result was provided for inclusions with finite dimensional state spaces which
says that the approximation can be carried out over non-compact or infinite
intervals provided one does not insist on the same initial values. This note
extends the infinite-time relaxation theorem to the inclusions whose state
spaces are Banach spaces. To illustrate the motivations for studying such
approximation results, we briefly discuss a quick application of the result to
output stability and uniform output stability properties.
