  We extend the noncommutative L1-maximal ergodic inequality for semifinite von
Neumann algebras established by Yeadon in 1977 to the framework of
noncommutative L1-spaces associated with sigma-finite von Neumann algebras.
Since the semifnite case of this result is one of the two essential parts in
the proof of noncommutative maximal ergodic inequality for tracial Lp-spaces
(1<p<infinity) by Junge-Xu in 2007, we hope our result will be helpful to
establish a complete noncommutative maximal ergodic inequality for non-tracial
Lp-spaces in the future.
