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arXiv · 1502.06566

Weak Rational Ergodicity Does Not Imply Rational Ergodicity

Terrence M. Adams·Cesar E. Silva
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Abstract

We extend the notion of rational ergodicity to $\beta$-rational ergodicity for $\beta > 1$. Given $\beta \in \mathbb R$ such that $\beta > 1$, we construct an uncountable family of rank-one infinite measure preserving transformations that are weakly rationally ergodic, but are not $\beta$-rationally ergodic. The established notion of rational ergodicity corresponds to 2-rational ergodicity. Thus, this paper answers an open question by showing that weak rational ergodicity does not imply rational ergodicity.

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Terrence M. Adams, Cesar E. Silva. 2015-02-23. Weak Rational Ergodicity Does Not Imply Rational Ergodicity. https://arxiv.org/abs/1502.06566

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