Weighted ergodic theorems for Banach-Kantorovich lattice   $L_{p}(\hat{\nabla},\hat{\mu})$
  In the present paper we prove weighted ergodic theorems and multiparameter weighted ergodic theorems for positive contractions acting on $L_p(\hat{\nabla},\hat{\mu})$. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices. 
Inomjon Ganiev, Farrukh Mukhamedov
math.FA math.DS