General and weighted averages of admissible superadditive processes

Abstract

It is shown that if $\{\mu_{n}\}$ is a sequence of measures good a.e. or resp. in the p-mean for additive processes, then it is good a.e. or resp. in the p-mean, for the class of strongly bounded admissible superadditive processes. Using the method developed, it is shown also that weighted averages of strongly bounded admissible superadditive processes converge a.e. or in the p-mean for weights that are good a.e. or in the p-mean for additive processes.