Semigroups of endomorphisms of Lebesgue space with strict ergodic properties.

In the paper systems of endomorphisms $T_\alpha , \alpha\in\Lambda$, such that their products generate semigroups: any seguence of the semigroup is exact (ergodic, nonergodic), are considered. Natural extensions of such semigroups are groups of automorphisms with strict ergodic properties.