Abstract:Every aperiodic endomorphism $f$ of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator $\beta $ such that $k_f\leq card \beta \leq k_f+1$. This is the best estimate for the minimal cardinality of a 1-sided generator. The above result is the generalization of the analogous one for ergodic case.
Keywords: aperiodic endomorphism, 1-sided generator
AMS Subject Classification: 28D05