Pointwise weighted vector ergodic theorem in
L1(X)
K. El Berdan
Abstract.
In this paper we prove the almost everywhere convergence of weighted
multiparameter averages of linear surjective isometries in $L^{1}(X)$ and
power bounded in $L^{p}(X),1\le p\leq \infty .$
Compressed Postscript 
