Recurrence properties of superadditive processes and universally good weights

Abstract

In this article recurrence properties of a class of strongly bounded superadditive processes are studied at some length. In particular, four generalizations of Fürstenberg’s multiple recurrence theorem are extended to the setting of such superadditive processes. Having these recurrence properties in hand, it is observed that such superadditive processes define universally good weights for various type of ergodic averages.