It is shown that if two functions share the same uncentered (two-sided) ergodic maximal function, then they are equal almost everywhere.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-5,
author = {Paul Alton Hagelstein},
title = {On the uniqueness of the uncentered ergodic maximal function},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {81-90},
zbl = {1069.28010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-5}
}
Paul Alton Hagelstein. On the uniqueness of the uncentered ergodic maximal function. Fundamenta Mathematicae, Tome 184 (2004) pp. 81-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-5/