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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
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