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On sequences of density zero in ergodic theory. (English) Zbl 0587.28013
Contemp. Math. 26, 49-60 (1984).
A sequence $$m_1<m_2<\ldots$$ of positive integers is “good universal” if for every automorphism $$T$$ of any probability space, the sequence of functions $$\{p^{-1}\sum^{p}_{k=1}f\circ T^{m_k}\}$$ converges a.e., for every $$L^1$$ function $$f$$. If for every aperiodic automorphism of any probability space, the preceding sequence does not converge a.e. for at least one $$L^1$$ function $$f$$, the sequence $$(m_k)$$ is “bad universal.” The authors find a class of “good universal” sequences and a class of ’“bad universal” sequences not heretofore known.
For the entire collection see [Zbl 0523.00008].

MSC:
 28D05 Measure-preserving transformations
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