Abstract
In the previous chapters we saw that recurrent transformations do not accept wandering sets. An important subset of the recurrent transformations are the ergodic ones that do not have a finite invariant and equivalent measure. These transformations also do not accept wandering sets, yet they must necessarily accept ww and eww sets. For infinite ergodic transformations the existence of ww sets is a significant property and reflects the subtle features of these transformations. In this chapter we discuss the strong bond that exists between infinite ergodic transformations and ww or eww sequences.
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Eigen, S., Hajian, A., Ito, Y., Prasad, V. (2014). Infinite Ergodic Transformations. In: Weakly Wandering Sequences in Ergodic Theory. Springer Monographs in Mathematics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55108-9_3
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DOI: https://doi.org/10.1007/978-4-431-55108-9_3
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