  It is proved that, in the Misra-Prigogine-Courbage Theory of Irreversibility
using the Internal Time superoperator, fixing its associated non-unitary
transformation $\Lambda$, amounts to rigging the corresponding
Hilbert-Liouville space. More precisely, it is demonstrated that any $\Lambda $
determinates three canonical riggings of the Liouville space $\QTR{cal}{L}$: a
first one with a Hilbert space with a norm greater than the relative one from
$\QTR{cal}{L}$; a second one with a $\sigma $-Hilbertian space, which is a
K\"{o}the space if $\Lambda$ is compact and is a nuclear space if $\Lambda$ has
certain nuclear properties; and finally a third one with a smaller $\sigma
$-Hilbertian space with a still stronger topology which is nuclear if $\Lambda
^{n}$ is Hilbert-Schmidt, for some positive integer n. Viceversa: any rigging
of this type, originated in a dynamical system having an Internal Time
superoperator, defines a $\Lambda$ in a canonical way.
