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/