On weakly mixing and doubly ergodic nonsingular actions

Sarah Iams, et al. "On weakly mixing and doubly ergodic nonsingular actions." Colloquium Mathematicae 103.2 (2005): 247-264. <http://eudml.org/doc/283922>.

@article{SarahIams2005,
abstract = {We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving flow whose cartesian square is ergodic.},
author = {Sarah Iams, Brian Katz, Cesar E. Silva, Brian Street, Kirsten Wickelgren},
journal = {Colloquium Mathematicae},
keywords = {weakly mixing; doubly ergodic; measure-preserving transformation; action of Polish groups},
language = {eng},
number = {2},
pages = {247-264},
title = {On weakly mixing and doubly ergodic nonsingular actions},
url = {http://eudml.org/doc/283922},
volume = {103},
year = {2005},
}

TY - JOUR
AU - Sarah Iams
AU - Brian Katz
AU - Cesar E. Silva
AU - Brian Street
AU - Kirsten Wickelgren
TI - On weakly mixing and doubly ergodic nonsingular actions
JO - Colloquium Mathematicae
PY - 2005
VL - 103
IS - 2
SP - 247
EP - 264
AB - We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving flow whose cartesian square is ergodic.
LA - eng
KW - weakly mixing; doubly ergodic; measure-preserving transformation; action of Polish groups
UR - http://eudml.org/doc/283922
ER -