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Analysis and Probability by Aurel Spataru

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Chapter 12

Ergodicity, Mixing, and Stationarity

The classical ergodic theorems for measure-preserving transformations and their role in the theory of stationary sequences are the ultimate objectives of this chapter. To this end, a remarkable mathematical machinery is first built up, and a number of preliminary and adjacent results are established. Some topics on measure-preserving transformations such as weak-mixing and strong-mixing are also discussed.

31 Ergodicity and Mixing

The word “ergodic” hints at the origins in statistical mechanics. The main purpose of this section is to formulate and prove the most important classical ergodic theorems. To this end, we first introduce and discuss basic concepts such as measure-preserving transformation, ...

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