Ergodic Theoems for almost additive functions

The talk covers the long-term behaviour of measure preserving dynamical systems induced by amenable groups acting on probability spaces. We start with an introduction in the world of classic ergodic theorems. Some of those latter statements can be interpreted as "laws of large numbers" from statistics applied in a general setting of group dynamics. This leads to the notion of almost-additive Banach space-valued set functions, with their normalized version converging along Folner sequences. We present the corresponding abstact mean ergodic theorem and as an application, we mention the pointwise almost everywhere convergence of bounded, additive processes.