Weighted ergodic theorem for contractions of Orlicz-Kantorovich lattice L_M(N,m)

In the present paper we prove a Besicovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices

Weight martingale-ergodic and ergodic-martingale theorems

In this paper we prove weighted martingale-ergodic and weighted ergodic-martingale theorems. Furthermore, analogous dominant and maximal inequalities for weighted martingale ergodic sequences and weighted ergodic martingale averages are also obtained