It is proved that the ergodic maximal operator is one-to-one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-2, author = {Lasha Ephremidze}, title = {On the uniqueness of the ergodic maximal function}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {217-228}, zbl = {1004.28010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-2} }
Lasha Ephremidze. On the uniqueness of the ergodic maximal function. Fundamenta Mathematicae, Tome 173 (2002) pp. 217-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-2/