A countable group Γ has the Haagerup approximation property if and only if the mixing actions are dense in the space of all actions of Γ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-4,
author = {Greg Hjorth},
title = {Mixing actions of groups with the Haagerup approximation property},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {47-56},
zbl = {1168.03036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-4}
}
Greg Hjorth. Mixing actions of groups with the Haagerup approximation property. Fundamenta Mathematicae, Tome 205 (2009) pp. 47-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-4/