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/