Abstract
This chapter focuses on stationary sequences. It is very easy to obtain laws of large numbers for stationary sequences. The chapter presents the most fundamental laws without any proof as consequences of the ergodic theorems and of the results on the representation of stationary sequences by measure-preserving transformations. The difficulties from the special point of view of probability theory lie in the investigation of the condition of ergodicity. An ergodic sequence can be always represented by a non-ergodic transformation. The chapter describes stationary sequences by measure-preserving transformations.
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