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Minimal generators for aperiodic endomorphisms. (English) Zbl 0840.28006
Summary: Every aperiodic endomorphism $$f$$ of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator $$\beta$$ such that $$k_f\leq \text{card } \beta\leq k_f+ 1$$. 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.

##### MSC:
 28D05 Measure-preserving transformations
##### Keywords:
aperiodic endomorphism; one-sided generator
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