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arXiv · 1512.09340

Strict Doubly Ergodic Infinite Transformations

Isaac Loh·Cesar E. Silva
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Abstract

We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite measure-preserving transformations to be (weak) doubly ergodic and for their $k$-fold cartesian product to be conservative. We also show that a (weak) doubly ergodic nonsingular group action is ergodic with isometric coefficients, and that the latter strictly implies W measurable sensitivity.

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Isaac Loh, Cesar E. Silva. 2016-10-19. Strict Doubly Ergodic Infinite Transformations. https://arxiv.org/abs/1512.09340

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