Ergodicity and conservativity of products of infinite transformations and their inverses. (English) Zbl 1359.37017
Summary: We construct a class of rank-one infinite measure-preserving transformations such that for each transformation \(T\) in the class, the cartesian product \(T\times T\) is ergodic, but the product \(T\times T^{-1}\) is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.
MSC:
| 37A40 | Nonsingular (and infinite-measure preserving) transformations |
| 37A05 | Dynamical aspects of measure-preserving transformations |
| 37A50 | Dynamical systems and their relations with probability theory and stochastic processes |
| 37A25 | Ergodicity, mixing, rates of mixing |
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