Vitali-type theorems for filter convergence related to vector   lattice-valued modulars and applications to stochastic processes
  A Vitali-type theorem for vector lattice-valued modulars with respect to filter convergence is proved. Some applications are given to modular convergence theorems for moment operatorsin the vector lattice setting, and also for the Brownian motion and related stochastic processes. 
Antonio Boccuto, Domenico Candeloro and Anna Rita Sambucini
math.FA