ERGODICITY AND CONSERVATIVITY OF PRODUCTS OF INFINITE TRANSFORMATIONS AND THEIR INVERSES

作者：Clancy Julien^*; Friedberg Rina^*; Kasmalkar Indraneel^*; Loh Isaac^*; Padurariu Tudor^*; Silva Cesar E^*; Vasudevan Sahana^*

来源：Colloquium Mathematicum, 2016, 143(2): 271-291.

DOI：10.4064/cm6482-10-2015

• infinite measure-preserving
• ergodic
• conservative
• inverse transformation
• rank-one

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T x T is ergodic, but the product T x 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.

• 出版日期2016