The uniqueness theorem for the ergodic maximal operator is proved in the continous case.
@article{urn:eudml:doc:44422,
title = {On the uniqueness of maximal operators for ergodic flows.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {15},
year = {2002},
pages = {75-84},
zbl = {1063.37001},
mrnumber = {MR1915216},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44422}
}
Ephremidze, Lasha. On the uniqueness of maximal operators for ergodic flows.. Revista Matemática de la Universidad Complutense de Madrid, Tome 15 (2002) pp. 75-84. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44422/