Ergodicity and conservativity of products of infinite transformations and their inverses

• Autorzy: Julien Clancy , Rina Friedberg , Indraneel Kasmalkar , Isaac Loh , Tudor Pădurariu , Cesar E. Silva , Sahana Vasudevan
• Języki publikacji: EN

Abstrakty

EN

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T × T^{-1}$ 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.

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 37A05: Measure-preserving transformations
• 37A40: Nonsingular (and infinite-measure preserving) transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 2
• Strony: 271-291

Daty

wydano

2016

Twórcy

autor

Julien Clancy

• Yale University, New Haven, CT 06520, U.S.A.

autor

Rina Friedberg

• University of Chicago, Chicago, IL 60637, U.S.A.

autor

Indraneel Kasmalkar

• University of California, Berkeley, Berkeley, CA 94720, U.S.A.

autor

Isaac Loh

• Williams College, Williamstown, MA 01267, U.S.A.

autor

Tudor Pădurariu

• University of California, Los Angeles, CA 90095-1555, U.S.A.

autor

Cesar E. Silva

• Department of Mathematics, Williams College, Williamstown, MA 01267, U.S.A.

autor

Sahana Vasudevan

• Harvard University, Cambridge, MA 02138, U.S.A.

Identyfikatory

DOI

10.4064/cm6482-10-2015