We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9,
author = {Thierry de la Rue},
title = {An extension which is relatively twofold mixing but not threefold mixing},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {271-277},
zbl = {1067.37006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9}
}
Thierry de la Rue. An extension which is relatively twofold mixing but not threefold mixing. Colloquium Mathematicae, Tome 100 (2004) pp. 271-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9/